Hi.gher. Space

by **benb** » Tue Jan 21, 2014 7:25 pm

Hello world! This is my first post on this board and I hope you like (and can help improve) what I have to share. I've been working on a project called Hyperland that seeks to create an open source platform for 4D simulations. We have a working prototype of a visualization interface called the Double Rainbow Display; in addition to allowing users to investigate 4D scenes from various vantage points, users can also use it to translate and rotate 4D objects in 4D simulations.

For a basic, no-frills narrated overview/introduction of the basic setup, check out the video called "Escape from Fools' Prison: motion in simulated space" at http://youtu.be/wcUJ7GbMiDo

For a demonstration of translation and rotation with a bit more flair, check out this video called "4D Double Helix 3" at http://youtu.be/34LexlgbUg0

Thanks for reading this and for having such a cool online community!

by **quickfur** » Wed Jan 22, 2014 6:10 am

I watched the first part of the first video, but it wasn't clear to me how 4D is being represented here. It appears to have something to do with the "double rainbow display", but it wasn't explained what that means or how it works, so after a while I just got lost looking at shapes morphing beyond my comprehension. The use of line drawings also made it a bit difficult to tell what is being shown, although for the most part, it wasn't too difficult to figure out.

A more helpful 4D exploration that I found is John McIntosh's 4D maze, which uses 4D->3D projection. It was one of the first things that helped me truly visualize 4D. In spite of also being based on line-drawings, it uses a more direct analogy to how our own eyes see in 3D, and also offers stereoscopic rendering to help bring out the 3D depth in the projection images.

by **benb** » Wed Jan 22, 2014 1:44 pm

@quickfur: You are in luck! John McIntosh wrote the vast majority of the code that makes what you're seeing in that video possible; one can load the same file containing the "prison" with the yellow tesseracts outside of it using the traditional view from the 4D maze if one prefers. (The settings may be toggled for a variety of visualization options.) You can download the prison file from the Hyperland repo on GitHub and the code/app McIntosh wrote from https://osf.io/dxjeo/wiki/4DBlocks/

To learn more about how the Display works, this page should prove helpful: https://osf.io/dxjeo/wiki/DoubleRainbowDisplay/

To see one of the 4D mazes generated by McIntosh's program using an earlier iteration of the Double Rainbow Display with a non-traditional projection, check out this video: http://youtu.be/3NZGDvghUL8

That said, a limitation of the 4D Maze as well as the Prison video is that is does not demonstrate the interactive capacity of the simulation interface as it currently exists; at present, one may navigate the 4D manifold using the code McIntosh generated (which allows users like you or I to populate that manifold with various items through some file generation of our own). One can also select and move items in that 4D environment.

by **quickfur** » Thu Jan 23, 2014 3:47 am

benb wrote:[...]To learn more about how the Display works, this page should prove helpful: https://osf.io/dxjeo/wiki/DoubleRainbowDisplay/
[...]

Thanks, that cleared things up! It's certainly an interesting take on 4D visualization, I must say. So it would amount to having two 3D views at 90° to each other. A clever way to get us 3D-bound people to work directly with 4D.

I admit I'm rather a fan of the 4D->3D perspective projection method, as McIntosh's 4D maze uses (and also his 4D Blocks -- just noticed that yesterday!). How well does the double rainbow display work with non-tesseractic objects, like, say, the 120-cell? I must say I still find the 3D projection of the 120-cell (with suitable back face culling) easiest to comprehend as a whole.

by **benb** » Thu Jan 23, 2014 11:56 am

@quickfur: Your curiosity is contagious. I have yet to write the code for the 120-cell, though I am interested. If you wouldn't mind/would like to, please contribute a 120-cell geom file to a repository (or provide the coordinates for its vertices with a recommended minimum of one unit between each vertex; someone else can create the geom file from that). Once we have the file for the 120-cell, it can be loaded and viewed using the traditional stereo vision/crosseye method and/or the double rainbow way.

by **Klitzing** » Thu Jan 23, 2014 1:28 pm

Easy.
Let t = (1+sqrt(5))/2.
Then ex = hexacosachoron = x3o3o5o will have the vertex set:

(t, 0, 0, 0) & all permutations & all changes of sign
(then providing the vertices of a scaled, vertex inscribed hex = hexadecachoron = x3o3o4o)
(t/2, t/2, t/2, t/2) & all changes of sign
(then providing the vertices of a scaled, vertex inscribed tes = tesseract = x4o3o3o)
(t^2/2, t/2, 1/2,0) & ~~all~~ even permutations & all changes of sign
(then providing the vertices of a vertex inscribed sadi = snub icositetrachoron = s3s4o3o)

Edges then occur wherever 2 such vertices are one unit apart, i.e. have distance 1.

Edit: oops, that was the 600-cell instead, not the 120-cell, sorry :oops:

Edit: The correct form is 'even permutations' not all' (Wendy) [fixed braino]
Edit: Thanks Wendy for checking it, That indeed was a typo of mine.
--- rk

by **quickfur** » Thu Jan 23, 2014 4:02 pm

benb wrote:@quickfur: Your curiosity is contagious. I have yet to write the code for the 120-cell, though I am interested. If you wouldn't mind/would like to, please contribute a 120-cell geom file to a repository (or provide the coordinates for its vertices with a recommended minimum of one unit between each vertex; someone else can create the geom file from that). Once we have the file for the 120-cell, it can be loaded and viewed using the traditional stereo vision/crosseye method and/or the double rainbow way.

You can get the 120-cell's coordinates, as well as many projections I made of it, on my 120-cell page. Here's a favorite of mine:

by **wendy** » Fri Jan 24, 2014 10:13 am

The vertices of x5o3o3o by coxeter is in 'even permutations, all changes of sign'

The edge is 2vv. ff = f*f = 2.618, r5 = sqrt(5)= 2.236, 2 = 2.000, f = 1.618, 1 = 1.000, v = 0.618, vv = v*v, = 0.382.

Vertex count and drawdown in base 120.

ff, v, v, v gives 4*16 = 64 500-64 = 456
ff, 1, vv, 0 gives 12*8 = 96 456 - 96 = 380
r5,1,1,1 gives 4*64 = 64 380-64 = 316
r5,f,v,0 gives 12*8 = 96, 316 - 96 = 240
2,2,0,0 gives 6*4 = 24 240-24 = 216
2,f,1,v gives 12*16 216 - 172 = 64
f,f,f,v gives 4*16 = 64 64 - 64 = 0

The vertices correspond to (vv)2o3o5(vv) + (v)2o3o5(v) + (v)2o3(v)5o + (vv)2o3o5x + (v)2x(v)3o5(v). This cryptic comment, says that if you calculate a coordinate for a prism of the first figure to size whateve, and the thing on the other side of the '2', you get a prism that's part of the twelftychoron. All sections won't get you a complete set, but you can use pyritochoral coordinates (ie even permutations, all changes of sign), to fill in the rest.

by **quickfur** » Fri Jan 24, 2014 4:33 pm

Alright, to make it really easy, here's the raw coordinates of the 120-cell, in convenient floating-point format, with no need of tricky permutation operations and all that jazz, and scaled so that it is exactly edge length 1:

Code: Select all: <2.61803398874989490253, 2.61803398874989490253, 0.00000000000000000000, 0.00000000000000000000> <2.61803398874989490253, -2.61803398874989490253, 0.00000000000000000000, 0.00000000000000000000> <-2.61803398874989490253, 2.61803398874989490253, 0.00000000000000000000, 0.00000000000000000000> <-2.61803398874989490253, -2.61803398874989490253, 0.00000000000000000000, 0.00000000000000000000> <0.00000000000000000000, 0.00000000000000000000, 2.61803398874989490253, 2.61803398874989490253> <0.00000000000000000000, 0.00000000000000000000, 2.61803398874989490253, -2.61803398874989490253> <0.00000000000000000000, 0.00000000000000000000, -2.61803398874989490253, 2.61803398874989490253> <0.00000000000000000000, 0.00000000000000000000, -2.61803398874989490253, -2.61803398874989490253> <0.00000000000000000000, 2.61803398874989490253, 0.00000000000000000000, 2.61803398874989490253> <0.00000000000000000000, 2.61803398874989490253, 0.00000000000000000000, -2.61803398874989490253> 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<2.92705098312484235379, -1.30901699437494745126, -1.30901699437494745126, 1.30901699437494745126> <2.92705098312484235379, -1.30901699437494745126, -1.30901699437494745126, -1.30901699437494745126> <-2.92705098312484235379, 1.30901699437494745126, 1.30901699437494745126, 1.30901699437494745126> <-2.92705098312484235379, 1.30901699437494745126, 1.30901699437494745126, -1.30901699437494745126> <-2.92705098312484235379, 1.30901699437494745126, -1.30901699437494745126, 1.30901699437494745126> <-2.92705098312484235379, 1.30901699437494745126, -1.30901699437494745126, -1.30901699437494745126> <-2.92705098312484235379, -1.30901699437494745126, 1.30901699437494745126, 1.30901699437494745126> <-2.92705098312484235379, -1.30901699437494745126, 1.30901699437494745126, -1.30901699437494745126> <-2.92705098312484235379, -1.30901699437494745126, -1.30901699437494745126, 1.30901699437494745126> <-2.92705098312484235379, -1.30901699437494745126, -1.30901699437494745126, -1.30901699437494745126> <1.30901699437494745126, 1.30901699437494745126, 1.30901699437494745126, 2.92705098312484235379> <1.30901699437494745126, 1.30901699437494745126, 1.30901699437494745126, -2.92705098312484235379> <1.30901699437494745126, 1.30901699437494745126, -1.30901699437494745126, 2.92705098312484235379> <1.30901699437494745126, 1.30901699437494745126, -1.30901699437494745126, -2.92705098312484235379> <1.30901699437494745126, -1.30901699437494745126, 1.30901699437494745126, 2.92705098312484235379> <1.30901699437494745126, -1.30901699437494745126, 1.30901699437494745126, -2.92705098312484235379> <1.30901699437494745126, -1.30901699437494745126, -1.30901699437494745126, 2.92705098312484235379> <1.30901699437494745126, -1.30901699437494745126, -1.30901699437494745126, -2.92705098312484235379> <-1.30901699437494745126, 1.30901699437494745126, 1.30901699437494745126, 2.92705098312484235379> <-1.30901699437494745126, 1.30901699437494745126, 1.30901699437494745126, -2.92705098312484235379> <-1.30901699437494745126, 1.30901699437494745126, -1.30901699437494745126, 2.92705098312484235379> <-1.30901699437494745126, 1.30901699437494745126, -1.30901699437494745126, -2.92705098312484235379> <-1.30901699437494745126, -1.30901699437494745126, 1.30901699437494745126, 2.92705098312484235379> <-1.30901699437494745126, -1.30901699437494745126, 1.30901699437494745126, -2.92705098312484235379> <-1.30901699437494745126, -1.30901699437494745126, -1.30901699437494745126, 2.92705098312484235379> <-1.30901699437494745126, -1.30901699437494745126, -1.30901699437494745126, -2.92705098312484235379> <1.30901699437494745126, 1.30901699437494745126, 2.92705098312484235379, 1.30901699437494745126> <1.30901699437494745126, 1.30901699437494745126, 2.92705098312484235379, -1.30901699437494745126> <1.30901699437494745126, 1.30901699437494745126, -2.92705098312484235379, 1.30901699437494745126> <1.30901699437494745126, 1.30901699437494745126, -2.92705098312484235379, -1.30901699437494745126> <1.30901699437494745126, -1.30901699437494745126, 2.92705098312484235379, 1.30901699437494745126> <1.30901699437494745126, -1.30901699437494745126, 2.92705098312484235379, -1.30901699437494745126> <1.30901699437494745126, -1.30901699437494745126, -2.92705098312484235379, 1.30901699437494745126> <1.30901699437494745126, -1.30901699437494745126, -2.92705098312484235379, -1.30901699437494745126> <-1.30901699437494745126, 1.30901699437494745126, 2.92705098312484235379, 1.30901699437494745126> <-1.30901699437494745126, 1.30901699437494745126, 2.92705098312484235379, -1.30901699437494745126> <-1.30901699437494745126, 1.30901699437494745126, -2.92705098312484235379, 1.30901699437494745126> <-1.30901699437494745126, 1.30901699437494745126, -2.92705098312484235379, -1.30901699437494745126> <-1.30901699437494745126, -1.30901699437494745126, 2.92705098312484235379, 1.30901699437494745126> <-1.30901699437494745126, -1.30901699437494745126, 2.92705098312484235379, -1.30901699437494745126> <-1.30901699437494745126, -1.30901699437494745126, -2.92705098312484235379, 1.30901699437494745126> <-1.30901699437494745126, -1.30901699437494745126, -2.92705098312484235379, -1.30901699437494745126> <1.30901699437494745126, 2.92705098312484235379, 1.30901699437494745126, 1.30901699437494745126> <1.30901699437494745126, 2.92705098312484235379, 1.30901699437494745126, -1.30901699437494745126> <1.30901699437494745126, 2.92705098312484235379, -1.30901699437494745126, 1.30901699437494745126> <1.30901699437494745126, 2.92705098312484235379, -1.30901699437494745126, -1.30901699437494745126> <1.30901699437494745126, -2.92705098312484235379, 1.30901699437494745126, 1.30901699437494745126> <1.30901699437494745126, -2.92705098312484235379, 1.30901699437494745126, -1.30901699437494745126> <1.30901699437494745126, -2.92705098312484235379, -1.30901699437494745126, 1.30901699437494745126> <1.30901699437494745126, -2.92705098312484235379, -1.30901699437494745126, -1.30901699437494745126> <-1.30901699437494745126, 2.92705098312484235379, 1.30901699437494745126, 1.30901699437494745126> <-1.30901699437494745126, 2.92705098312484235379, 1.30901699437494745126, -1.30901699437494745126> <-1.30901699437494745126, 2.92705098312484235379, -1.30901699437494745126, 1.30901699437494745126> <-1.30901699437494745126, 2.92705098312484235379, -1.30901699437494745126, -1.30901699437494745126> <-1.30901699437494745126, -2.92705098312484235379, 1.30901699437494745126, 1.30901699437494745126> <-1.30901699437494745126, -2.92705098312484235379, 1.30901699437494745126, -1.30901699437494745126> <-1.30901699437494745126, -2.92705098312484235379, -1.30901699437494745126, 1.30901699437494745126> <-1.30901699437494745126, -2.92705098312484235379, -1.30901699437494745126, -1.30901699437494745126> <2.11803398874989490253, 2.11803398874989490253, 2.11803398874989490253, 0.50000000000000000000> <2.11803398874989490253, 2.11803398874989490253, 2.11803398874989490253, -0.50000000000000000000> 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<-2.11803398874989490253, -2.11803398874989490253, 2.11803398874989490253, 0.50000000000000000000> <-2.11803398874989490253, -2.11803398874989490253, 2.11803398874989490253, -0.50000000000000000000> <-2.11803398874989490253, -2.11803398874989490253, -2.11803398874989490253, 0.50000000000000000000> <-2.11803398874989490253, -2.11803398874989490253, -2.11803398874989490253, -0.50000000000000000000> <0.50000000000000000000, 2.11803398874989490253, 2.11803398874989490253, 2.11803398874989490253> <0.50000000000000000000, 2.11803398874989490253, 2.11803398874989490253, -2.11803398874989490253> <0.50000000000000000000, 2.11803398874989490253, -2.11803398874989490253, 2.11803398874989490253> <0.50000000000000000000, 2.11803398874989490253, -2.11803398874989490253, -2.11803398874989490253> <0.50000000000000000000, -2.11803398874989490253, 2.11803398874989490253, 2.11803398874989490253> <0.50000000000000000000, -2.11803398874989490253, 2.11803398874989490253, -2.11803398874989490253> <0.50000000000000000000, -2.11803398874989490253, -2.11803398874989490253, 2.11803398874989490253> <0.50000000000000000000, -2.11803398874989490253, -2.11803398874989490253, -2.11803398874989490253> <-0.50000000000000000000, 2.11803398874989490253, 2.11803398874989490253, 2.11803398874989490253> <-0.50000000000000000000, 2.11803398874989490253, 2.11803398874989490253, -2.11803398874989490253> <-0.50000000000000000000, 2.11803398874989490253, -2.11803398874989490253, 2.11803398874989490253> <-0.50000000000000000000, 2.11803398874989490253, -2.11803398874989490253, -2.11803398874989490253> <-0.50000000000000000000, -2.11803398874989490253, 2.11803398874989490253, 2.11803398874989490253> <-0.50000000000000000000, -2.11803398874989490253, 2.11803398874989490253, -2.11803398874989490253> <-0.50000000000000000000, -2.11803398874989490253, -2.11803398874989490253, 2.11803398874989490253> <-0.50000000000000000000, -2.11803398874989490253, -2.11803398874989490253, -2.11803398874989490253> <2.11803398874989490253, 0.50000000000000000000, 2.11803398874989490253, 2.11803398874989490253> <2.11803398874989490253, 0.50000000000000000000, 2.11803398874989490253, -2.11803398874989490253> <2.11803398874989490253, 0.50000000000000000000, -2.11803398874989490253, 2.11803398874989490253> <2.11803398874989490253, 0.50000000000000000000, -2.11803398874989490253, -2.11803398874989490253> <2.11803398874989490253, -0.50000000000000000000, 2.11803398874989490253, 2.11803398874989490253> <2.11803398874989490253, -0.50000000000000000000, 2.11803398874989490253, -2.11803398874989490253> <2.11803398874989490253, -0.50000000000000000000, -2.11803398874989490253, 2.11803398874989490253> <2.11803398874989490253, -0.50000000000000000000, -2.11803398874989490253, -2.11803398874989490253> <-2.11803398874989490253, 0.50000000000000000000, 2.11803398874989490253, 2.11803398874989490253> <-2.11803398874989490253, 0.50000000000000000000, 2.11803398874989490253, -2.11803398874989490253> <-2.11803398874989490253, 0.50000000000000000000, -2.11803398874989490253, 2.11803398874989490253> <-2.11803398874989490253, 0.50000000000000000000, -2.11803398874989490253, -2.11803398874989490253> <-2.11803398874989490253, -0.50000000000000000000, 2.11803398874989490253, 2.11803398874989490253> <-2.11803398874989490253, -0.50000000000000000000, 2.11803398874989490253, -2.11803398874989490253> <-2.11803398874989490253, -0.50000000000000000000, -2.11803398874989490253, 2.11803398874989490253> <-2.11803398874989490253, -0.50000000000000000000, -2.11803398874989490253, -2.11803398874989490253> <2.11803398874989490253, 2.11803398874989490253, 0.50000000000000000000, 2.11803398874989490253> <2.11803398874989490253, 2.11803398874989490253, 0.50000000000000000000, -2.11803398874989490253> <2.11803398874989490253, 2.11803398874989490253, -0.50000000000000000000, 2.11803398874989490253> <2.11803398874989490253, 2.11803398874989490253, -0.50000000000000000000, -2.11803398874989490253> <2.11803398874989490253, -2.11803398874989490253, 0.50000000000000000000, 2.11803398874989490253> <2.11803398874989490253, -2.11803398874989490253, 0.50000000000000000000, -2.11803398874989490253> <2.11803398874989490253, -2.11803398874989490253, -0.50000000000000000000, 2.11803398874989490253> <2.11803398874989490253, -2.11803398874989490253, -0.50000000000000000000, -2.11803398874989490253> <-2.11803398874989490253, 2.11803398874989490253, 0.50000000000000000000, 2.11803398874989490253> <-2.11803398874989490253, 2.11803398874989490253, 0.50000000000000000000, -2.11803398874989490253> <-2.11803398874989490253, 2.11803398874989490253, -0.50000000000000000000, 2.11803398874989490253> <-2.11803398874989490253, 2.11803398874989490253, -0.50000000000000000000, -2.11803398874989490253> <-2.11803398874989490253, -2.11803398874989490253, 0.50000000000000000000, 2.11803398874989490253> <-2.11803398874989490253, -2.11803398874989490253, 0.50000000000000000000, -2.11803398874989490253> <-2.11803398874989490253, -2.11803398874989490253, -0.50000000000000000000, 2.11803398874989490253> <-2.11803398874989490253, -2.11803398874989490253, -0.50000000000000000000, -2.11803398874989490253> <3.42705098312484235379, 0.80901699437494756229, 0.80901699437494756229, 0.80901699437494756229> <3.42705098312484235379, 0.80901699437494756229, 0.80901699437494756229, -0.80901699437494756229> <3.42705098312484235379, 0.80901699437494756229, -0.80901699437494756229, 0.80901699437494756229> <3.42705098312484235379, 0.80901699437494756229, -0.80901699437494756229, -0.80901699437494756229> <3.42705098312484235379, -0.80901699437494756229, 0.80901699437494756229, 0.80901699437494756229> <3.42705098312484235379, -0.80901699437494756229, 0.80901699437494756229, -0.80901699437494756229> <3.42705098312484235379, -0.80901699437494756229, -0.80901699437494756229, 0.80901699437494756229> <3.42705098312484235379, -0.80901699437494756229, -0.80901699437494756229, -0.80901699437494756229> <-3.42705098312484235379, 0.80901699437494756229, 0.80901699437494756229, 0.80901699437494756229> <-3.42705098312484235379, 0.80901699437494756229, 0.80901699437494756229, -0.80901699437494756229> <-3.42705098312484235379, 0.80901699437494756229, -0.80901699437494756229, 0.80901699437494756229> <-3.42705098312484235379, 0.80901699437494756229, -0.80901699437494756229, -0.80901699437494756229> <-3.42705098312484235379, -0.80901699437494756229, 0.80901699437494756229, 0.80901699437494756229> <-3.42705098312484235379, -0.80901699437494756229, 0.80901699437494756229, -0.80901699437494756229> <-3.42705098312484235379, -0.80901699437494756229, -0.80901699437494756229, 0.80901699437494756229> <-3.42705098312484235379, -0.80901699437494756229, -0.80901699437494756229, -0.80901699437494756229> <0.80901699437494756229, 0.80901699437494756229, 0.80901699437494756229, 3.42705098312484235379> <0.80901699437494756229, 0.80901699437494756229, 0.80901699437494756229, -3.42705098312484235379> <0.80901699437494756229, 0.80901699437494756229, -0.80901699437494756229, 3.42705098312484235379> <0.80901699437494756229, 0.80901699437494756229, -0.80901699437494756229, -3.42705098312484235379> <0.80901699437494756229, -0.80901699437494756229, 0.80901699437494756229, 3.42705098312484235379> <0.80901699437494756229, -0.80901699437494756229, 0.80901699437494756229, -3.42705098312484235379> <0.80901699437494756229, -0.80901699437494756229, -0.80901699437494756229, 3.42705098312484235379> <0.80901699437494756229, -0.80901699437494756229, -0.80901699437494756229, -3.42705098312484235379> <-0.80901699437494756229, 0.80901699437494756229, 0.80901699437494756229, 3.42705098312484235379> <-0.80901699437494756229, 0.80901699437494756229, 0.80901699437494756229, -3.42705098312484235379> <-0.80901699437494756229, 0.80901699437494756229, -0.80901699437494756229, 3.42705098312484235379> <-0.80901699437494756229, 0.80901699437494756229, -0.80901699437494756229, -3.42705098312484235379> <-0.80901699437494756229, -0.80901699437494756229, 0.80901699437494756229, 3.42705098312484235379> <-0.80901699437494756229, -0.80901699437494756229, 0.80901699437494756229, -3.42705098312484235379> <-0.80901699437494756229, -0.80901699437494756229, -0.80901699437494756229, 3.42705098312484235379> <-0.80901699437494756229, -0.80901699437494756229, -0.80901699437494756229, -3.42705098312484235379> <0.80901699437494756229, 0.80901699437494756229, 3.42705098312484235379, 0.80901699437494756229> <0.80901699437494756229, 0.80901699437494756229, 3.42705098312484235379, -0.80901699437494756229> <0.80901699437494756229, 0.80901699437494756229, -3.42705098312484235379, 0.80901699437494756229> <0.80901699437494756229, 0.80901699437494756229, -3.42705098312484235379, -0.80901699437494756229> <0.80901699437494756229, -0.80901699437494756229, 3.42705098312484235379, 0.80901699437494756229> <0.80901699437494756229, -0.80901699437494756229, 3.42705098312484235379, -0.80901699437494756229> <0.80901699437494756229, -0.80901699437494756229, -3.42705098312484235379, 0.80901699437494756229> <0.80901699437494756229, -0.80901699437494756229, -3.42705098312484235379, -0.80901699437494756229> <-0.80901699437494756229, 0.80901699437494756229, 3.42705098312484235379, 0.80901699437494756229> <-0.80901699437494756229, 0.80901699437494756229, 3.42705098312484235379, -0.80901699437494756229> <-0.80901699437494756229, 0.80901699437494756229, -3.42705098312484235379, 0.80901699437494756229> <-0.80901699437494756229, 0.80901699437494756229, -3.42705098312484235379, -0.80901699437494756229> <-0.80901699437494756229, -0.80901699437494756229, 3.42705098312484235379, 0.80901699437494756229> <-0.80901699437494756229, -0.80901699437494756229, 3.42705098312484235379, -0.80901699437494756229> <-0.80901699437494756229, -0.80901699437494756229, -3.42705098312484235379, 0.80901699437494756229> <-0.80901699437494756229, -0.80901699437494756229, -3.42705098312484235379, -0.80901699437494756229> <0.80901699437494756229, 3.42705098312484235379, 0.80901699437494756229, 0.80901699437494756229> <0.80901699437494756229, 3.42705098312484235379, 0.80901699437494756229, -0.80901699437494756229> <0.80901699437494756229, 3.42705098312484235379, -0.80901699437494756229, 0.80901699437494756229> <0.80901699437494756229, 3.42705098312484235379, -0.80901699437494756229, -0.80901699437494756229> <0.80901699437494756229, -3.42705098312484235379, 0.80901699437494756229, 0.80901699437494756229> <0.80901699437494756229, -3.42705098312484235379, 0.80901699437494756229, -0.80901699437494756229> <0.80901699437494756229, -3.42705098312484235379, -0.80901699437494756229, 0.80901699437494756229> <0.80901699437494756229, -3.42705098312484235379, -0.80901699437494756229, -0.80901699437494756229> <-0.80901699437494756229, 3.42705098312484235379, 0.80901699437494756229, 0.80901699437494756229> <-0.80901699437494756229, 3.42705098312484235379, 0.80901699437494756229, -0.80901699437494756229> <-0.80901699437494756229, 3.42705098312484235379, -0.80901699437494756229, 0.80901699437494756229> <-0.80901699437494756229, 3.42705098312484235379, -0.80901699437494756229, -0.80901699437494756229> <-0.80901699437494756229, -3.42705098312484235379, 0.80901699437494756229, 0.80901699437494756229> <-0.80901699437494756229, -3.42705098312484235379, 0.80901699437494756229, -0.80901699437494756229> <-0.80901699437494756229, -3.42705098312484235379, -0.80901699437494756229, 0.80901699437494756229> <-0.80901699437494756229, -3.42705098312484235379, -0.80901699437494756229, -0.80901699437494756229> <3.42705098312484235379, 0.50000000000000000000, 1.30901699437494745126, 0.00000000000000000000> <3.42705098312484235379, 0.50000000000000000000, -1.30901699437494745126, 0.00000000000000000000> <3.42705098312484235379, -0.50000000000000000000, 1.30901699437494745126, 0.00000000000000000000> <3.42705098312484235379, -0.50000000000000000000, -1.30901699437494745126, 0.00000000000000000000> <-3.42705098312484235379, 0.50000000000000000000, 1.30901699437494745126, 0.00000000000000000000> <-3.42705098312484235379, 0.50000000000000000000, -1.30901699437494745126, 0.00000000000000000000> <-3.42705098312484235379, -0.50000000000000000000, 1.30901699437494745126, 0.00000000000000000000> <-3.42705098312484235379, -0.50000000000000000000, -1.30901699437494745126, 0.00000000000000000000> <3.42705098312484235379, 1.30901699437494745126, 0.00000000000000000000, 0.50000000000000000000> <3.42705098312484235379, 1.30901699437494745126, 0.00000000000000000000, -0.50000000000000000000> <3.42705098312484235379, -1.30901699437494745126, 0.00000000000000000000, 0.50000000000000000000> <3.42705098312484235379, -1.30901699437494745126, 0.00000000000000000000, -0.50000000000000000000> <-3.42705098312484235379, 1.30901699437494745126, 0.00000000000000000000, 0.50000000000000000000> <-3.42705098312484235379, 1.30901699437494745126, 0.00000000000000000000, -0.50000000000000000000> <-3.42705098312484235379, -1.30901699437494745126, 0.00000000000000000000, 0.50000000000000000000> <-3.42705098312484235379, -1.30901699437494745126, 0.00000000000000000000, -0.50000000000000000000> <0.00000000000000000000, 0.50000000000000000000, 3.42705098312484235379, 1.30901699437494745126> <0.00000000000000000000, 0.50000000000000000000, 3.42705098312484235379, -1.30901699437494745126> <0.00000000000000000000, 0.50000000000000000000, -3.42705098312484235379, 1.30901699437494745126> <0.00000000000000000000, 0.50000000000000000000, -3.42705098312484235379, -1.30901699437494745126> <0.00000000000000000000, -0.50000000000000000000, 3.42705098312484235379, 1.30901699437494745126> <0.00000000000000000000, -0.50000000000000000000, 3.42705098312484235379, -1.30901699437494745126> <0.00000000000000000000, -0.50000000000000000000, -3.42705098312484235379, 1.30901699437494745126> <0.00000000000000000000, -0.50000000000000000000, -3.42705098312484235379, -1.30901699437494745126> <0.00000000000000000000, 1.30901699437494745126, 0.50000000000000000000, 3.42705098312484235379> <0.00000000000000000000, 1.30901699437494745126, 0.50000000000000000000, -3.42705098312484235379> <0.00000000000000000000, 1.30901699437494745126, -0.50000000000000000000, 3.42705098312484235379> <0.00000000000000000000, 1.30901699437494745126, -0.50000000000000000000, -3.42705098312484235379> <0.00000000000000000000, -1.30901699437494745126, 0.50000000000000000000, 3.42705098312484235379> <0.00000000000000000000, -1.30901699437494745126, 0.50000000000000000000, -3.42705098312484235379> <0.00000000000000000000, -1.30901699437494745126, -0.50000000000000000000, 3.42705098312484235379> <0.00000000000000000000, -1.30901699437494745126, -0.50000000000000000000, -3.42705098312484235379> <0.00000000000000000000, 3.42705098312484235379, 1.30901699437494745126, 0.50000000000000000000> <0.00000000000000000000, 3.42705098312484235379, 1.30901699437494745126, -0.50000000000000000000> <0.00000000000000000000, 3.42705098312484235379, -1.30901699437494745126, 0.50000000000000000000> <0.00000000000000000000, 3.42705098312484235379, -1.30901699437494745126, -0.50000000000000000000> <0.00000000000000000000, -3.42705098312484235379, 1.30901699437494745126, 0.50000000000000000000> <0.00000000000000000000, -3.42705098312484235379, 1.30901699437494745126, -0.50000000000000000000> <0.00000000000000000000, -3.42705098312484235379, -1.30901699437494745126, 0.50000000000000000000> <0.00000000000000000000, -3.42705098312484235379, -1.30901699437494745126, -0.50000000000000000000> <0.50000000000000000000, 0.00000000000000000000, 1.30901699437494745126, 3.42705098312484235379> <0.50000000000000000000, 0.00000000000000000000, 1.30901699437494745126, -3.42705098312484235379> <0.50000000000000000000, 0.00000000000000000000, -1.30901699437494745126, 3.42705098312484235379> <0.50000000000000000000, 0.00000000000000000000, -1.30901699437494745126, -3.42705098312484235379> <-0.50000000000000000000, 0.00000000000000000000, 1.30901699437494745126, 3.42705098312484235379> <-0.50000000000000000000, 0.00000000000000000000, 1.30901699437494745126, -3.42705098312484235379> <-0.50000000000000000000, 0.00000000000000000000, -1.30901699437494745126, 3.42705098312484235379> <-0.50000000000000000000, 0.00000000000000000000, -1.30901699437494745126, -3.42705098312484235379> <0.50000000000000000000, 1.30901699437494745126, 3.42705098312484235379, 0.00000000000000000000> <0.50000000000000000000, 1.30901699437494745126, -3.42705098312484235379, 0.00000000000000000000> <0.50000000000000000000, -1.30901699437494745126, 3.42705098312484235379, 0.00000000000000000000> <0.50000000000000000000, -1.30901699437494745126, -3.42705098312484235379, 0.00000000000000000000> <-0.50000000000000000000, 1.30901699437494745126, 3.42705098312484235379, 0.00000000000000000000> <-0.50000000000000000000, 1.30901699437494745126, -3.42705098312484235379, 0.00000000000000000000> <-0.50000000000000000000, -1.30901699437494745126, 3.42705098312484235379, 0.00000000000000000000> <-0.50000000000000000000, -1.30901699437494745126, -3.42705098312484235379, 0.00000000000000000000> <0.50000000000000000000, 3.42705098312484235379, 0.00000000000000000000, 1.30901699437494745126> <0.50000000000000000000, 3.42705098312484235379, 0.00000000000000000000, -1.30901699437494745126> <0.50000000000000000000, -3.42705098312484235379, 0.00000000000000000000, 1.30901699437494745126> <0.50000000000000000000, -3.42705098312484235379, 0.00000000000000000000, -1.30901699437494745126> <-0.50000000000000000000, 3.42705098312484235379, 0.00000000000000000000, 1.30901699437494745126> <-0.50000000000000000000, 3.42705098312484235379, 0.00000000000000000000, -1.30901699437494745126> <-0.50000000000000000000, -3.42705098312484235379, 0.00000000000000000000, 1.30901699437494745126> <-0.50000000000000000000, -3.42705098312484235379, 0.00000000000000000000, -1.30901699437494745126> <1.30901699437494745126, 0.00000000000000000000, 3.42705098312484235379, 0.50000000000000000000> <1.30901699437494745126, 0.00000000000000000000, 3.42705098312484235379, -0.50000000000000000000> <1.30901699437494745126, 0.00000000000000000000, -3.42705098312484235379, 0.50000000000000000000> <1.30901699437494745126, 0.00000000000000000000, -3.42705098312484235379, -0.50000000000000000000> <-1.30901699437494745126, 0.00000000000000000000, 3.42705098312484235379, 0.50000000000000000000> <-1.30901699437494745126, 0.00000000000000000000, 3.42705098312484235379, -0.50000000000000000000> <-1.30901699437494745126, 0.00000000000000000000, -3.42705098312484235379, 0.50000000000000000000> <-1.30901699437494745126, 0.00000000000000000000, -3.42705098312484235379, -0.50000000000000000000> <1.30901699437494745126, 0.50000000000000000000, 0.00000000000000000000, 3.42705098312484235379> <1.30901699437494745126, 0.50000000000000000000, 0.00000000000000000000, -3.42705098312484235379> <1.30901699437494745126, -0.50000000000000000000, 0.00000000000000000000, 3.42705098312484235379> <1.30901699437494745126, -0.50000000000000000000, 0.00000000000000000000, -3.42705098312484235379> <-1.30901699437494745126, 0.50000000000000000000, 0.00000000000000000000, 3.42705098312484235379> <-1.30901699437494745126, 0.50000000000000000000, 0.00000000000000000000, -3.42705098312484235379> <-1.30901699437494745126, -0.50000000000000000000, 0.00000000000000000000, 3.42705098312484235379> <-1.30901699437494745126, -0.50000000000000000000, 0.00000000000000000000, -3.42705098312484235379> <1.30901699437494745126, 3.42705098312484235379, 0.50000000000000000000, 0.00000000000000000000> <1.30901699437494745126, 3.42705098312484235379, -0.50000000000000000000, 0.00000000000000000000> <1.30901699437494745126, -3.42705098312484235379, 0.50000000000000000000, 0.00000000000000000000> <1.30901699437494745126, -3.42705098312484235379, -0.50000000000000000000, 0.00000000000000000000> <-1.30901699437494745126, 3.42705098312484235379, 0.50000000000000000000, 0.00000000000000000000> <-1.30901699437494745126, 3.42705098312484235379, -0.50000000000000000000, 0.00000000000000000000> <-1.30901699437494745126, -3.42705098312484235379, 0.50000000000000000000, 0.00000000000000000000> <-1.30901699437494745126, -3.42705098312484235379, -0.50000000000000000000, 0.00000000000000000000> <3.42705098312484235379, 0.00000000000000000000, 0.50000000000000000000, 1.30901699437494745126> <3.42705098312484235379, 0.00000000000000000000, 0.50000000000000000000, -1.30901699437494745126> <3.42705098312484235379, 0.00000000000000000000, -0.50000000000000000000, 1.30901699437494745126> <3.42705098312484235379, 0.00000000000000000000, -0.50000000000000000000, -1.30901699437494745126> <-3.42705098312484235379, 0.00000000000000000000, 0.50000000000000000000, 1.30901699437494745126> <-3.42705098312484235379, 0.00000000000000000000, 0.50000000000000000000, -1.30901699437494745126> <-3.42705098312484235379, 0.00000000000000000000, -0.50000000000000000000, 1.30901699437494745126> <-3.42705098312484235379, 0.00000000000000000000, -0.50000000000000000000, -1.30901699437494745126> <2.92705098312484235379, 0.80901699437494756229, 2.11803398874989490253, 0.00000000000000000000> <2.92705098312484235379, 0.80901699437494756229, -2.11803398874989490253, 0.00000000000000000000> <2.92705098312484235379, -0.80901699437494756229, 2.11803398874989490253, 0.00000000000000000000> <2.92705098312484235379, -0.80901699437494756229, -2.11803398874989490253, 0.00000000000000000000> <-2.92705098312484235379, 0.80901699437494756229, 2.11803398874989490253, 0.00000000000000000000> <-2.92705098312484235379, 0.80901699437494756229, -2.11803398874989490253, 0.00000000000000000000> <-2.92705098312484235379, -0.80901699437494756229, 2.11803398874989490253, 0.00000000000000000000> <-2.92705098312484235379, -0.80901699437494756229, -2.11803398874989490253, 0.00000000000000000000> <2.92705098312484235379, 2.11803398874989490253, 0.00000000000000000000, 0.80901699437494756229> <2.92705098312484235379, 2.11803398874989490253, 0.00000000000000000000, -0.80901699437494756229> <2.92705098312484235379, -2.11803398874989490253, 0.00000000000000000000, 0.80901699437494756229> <2.92705098312484235379, -2.11803398874989490253, 0.00000000000000000000, -0.80901699437494756229> <-2.92705098312484235379, 2.11803398874989490253, 0.00000000000000000000, 0.80901699437494756229> <-2.92705098312484235379, 2.11803398874989490253, 0.00000000000000000000, -0.80901699437494756229> <-2.92705098312484235379, -2.11803398874989490253, 0.00000000000000000000, 0.80901699437494756229> <-2.92705098312484235379, -2.11803398874989490253, 0.00000000000000000000, -0.80901699437494756229> <0.00000000000000000000, 0.80901699437494756229, 2.92705098312484235379, 2.11803398874989490253> <0.00000000000000000000, 0.80901699437494756229, 2.92705098312484235379, -2.11803398874989490253> <0.00000000000000000000, 0.80901699437494756229, -2.92705098312484235379, 2.11803398874989490253> <0.00000000000000000000, 0.80901699437494756229, -2.92705098312484235379, -2.11803398874989490253> <0.00000000000000000000, -0.80901699437494756229, 2.92705098312484235379, 2.11803398874989490253> <0.00000000000000000000, -0.80901699437494756229, 2.92705098312484235379, -2.11803398874989490253> <0.00000000000000000000, -0.80901699437494756229, -2.92705098312484235379, 2.11803398874989490253> <0.00000000000000000000, -0.80901699437494756229, -2.92705098312484235379, -2.11803398874989490253> <0.00000000000000000000, 2.11803398874989490253, 0.80901699437494756229, 2.92705098312484235379> <0.00000000000000000000, 2.11803398874989490253, 0.80901699437494756229, -2.92705098312484235379> <0.00000000000000000000, 2.11803398874989490253, -0.80901699437494756229, 2.92705098312484235379> <0.00000000000000000000, 2.11803398874989490253, -0.80901699437494756229, -2.92705098312484235379> <0.00000000000000000000, -2.11803398874989490253, 0.80901699437494756229, 2.92705098312484235379> <0.00000000000000000000, -2.11803398874989490253, 0.80901699437494756229, -2.92705098312484235379> <0.00000000000000000000, -2.11803398874989490253, -0.80901699437494756229, 2.92705098312484235379> <0.00000000000000000000, -2.11803398874989490253, -0.80901699437494756229, -2.92705098312484235379> <0.00000000000000000000, 2.92705098312484235379, 2.11803398874989490253, 0.80901699437494756229> <0.00000000000000000000, 2.92705098312484235379, 2.11803398874989490253, -0.80901699437494756229> <0.00000000000000000000, 2.92705098312484235379, -2.11803398874989490253, 0.80901699437494756229> <0.00000000000000000000, 2.92705098312484235379, -2.11803398874989490253, -0.80901699437494756229> <0.00000000000000000000, -2.92705098312484235379, 2.11803398874989490253, 0.80901699437494756229> <0.00000000000000000000, -2.92705098312484235379, 2.11803398874989490253, -0.80901699437494756229> <0.00000000000000000000, -2.92705098312484235379, -2.11803398874989490253, 0.80901699437494756229> <0.00000000000000000000, -2.92705098312484235379, -2.11803398874989490253, -0.80901699437494756229> <0.80901699437494756229, 0.00000000000000000000, 2.11803398874989490253, 2.92705098312484235379> <0.80901699437494756229, 0.00000000000000000000, 2.11803398874989490253, -2.92705098312484235379> <0.80901699437494756229, 0.00000000000000000000, -2.11803398874989490253, 2.92705098312484235379> <0.80901699437494756229, 0.00000000000000000000, -2.11803398874989490253, -2.92705098312484235379> <-0.80901699437494756229, 0.00000000000000000000, 2.11803398874989490253, 2.92705098312484235379> <-0.80901699437494756229, 0.00000000000000000000, 2.11803398874989490253, -2.92705098312484235379> <-0.80901699437494756229, 0.00000000000000000000, -2.11803398874989490253, 2.92705098312484235379> <-0.80901699437494756229, 0.00000000000000000000, -2.11803398874989490253, -2.92705098312484235379> <0.80901699437494756229, 2.11803398874989490253, 2.92705098312484235379, 0.00000000000000000000> <0.80901699437494756229, 2.11803398874989490253, -2.92705098312484235379, 0.00000000000000000000> <0.80901699437494756229, -2.11803398874989490253, 2.92705098312484235379, 0.00000000000000000000> <0.80901699437494756229, -2.11803398874989490253, -2.92705098312484235379, 0.00000000000000000000> <-0.80901699437494756229, 2.11803398874989490253, 2.92705098312484235379, 0.00000000000000000000> <-0.80901699437494756229, 2.11803398874989490253, -2.92705098312484235379, 0.00000000000000000000> <-0.80901699437494756229, -2.11803398874989490253, 2.92705098312484235379, 0.00000000000000000000> <-0.80901699437494756229, -2.11803398874989490253, -2.92705098312484235379, 0.00000000000000000000> <0.80901699437494756229, 2.92705098312484235379, 0.00000000000000000000, 2.11803398874989490253> <0.80901699437494756229, 2.92705098312484235379, 0.00000000000000000000, -2.11803398874989490253> <0.80901699437494756229, -2.92705098312484235379, 0.00000000000000000000, 2.11803398874989490253> <0.80901699437494756229, -2.92705098312484235379, 0.00000000000000000000, -2.11803398874989490253> <-0.80901699437494756229, 2.92705098312484235379, 0.00000000000000000000, 2.11803398874989490253> <-0.80901699437494756229, 2.92705098312484235379, 0.00000000000000000000, -2.11803398874989490253> <-0.80901699437494756229, -2.92705098312484235379, 0.00000000000000000000, 2.11803398874989490253> <-0.80901699437494756229, -2.92705098312484235379, 0.00000000000000000000, -2.11803398874989490253> <2.11803398874989490253, 0.00000000000000000000, 2.92705098312484235379, 0.80901699437494756229> <2.11803398874989490253, 0.00000000000000000000, 2.92705098312484235379, -0.80901699437494756229> <2.11803398874989490253, 0.00000000000000000000, -2.92705098312484235379, 0.80901699437494756229> <2.11803398874989490253, 0.00000000000000000000, -2.92705098312484235379, -0.80901699437494756229> <-2.11803398874989490253, 0.00000000000000000000, 2.92705098312484235379, 0.80901699437494756229> <-2.11803398874989490253, 0.00000000000000000000, 2.92705098312484235379, -0.80901699437494756229> <-2.11803398874989490253, 0.00000000000000000000, -2.92705098312484235379, 0.80901699437494756229> <-2.11803398874989490253, 0.00000000000000000000, -2.92705098312484235379, -0.80901699437494756229> <2.11803398874989490253, 0.80901699437494756229, 0.00000000000000000000, 2.92705098312484235379> <2.11803398874989490253, 0.80901699437494756229, 0.00000000000000000000, -2.92705098312484235379> <2.11803398874989490253, -0.80901699437494756229, 0.00000000000000000000, 2.92705098312484235379> <2.11803398874989490253, -0.80901699437494756229, 0.00000000000000000000, -2.92705098312484235379> <-2.11803398874989490253, 0.80901699437494756229, 0.00000000000000000000, 2.92705098312484235379> <-2.11803398874989490253, 0.80901699437494756229, 0.00000000000000000000, -2.92705098312484235379> <-2.11803398874989490253, -0.80901699437494756229, 0.00000000000000000000, 2.92705098312484235379> <-2.11803398874989490253, -0.80901699437494756229, 0.00000000000000000000, -2.92705098312484235379> <2.11803398874989490253, 2.92705098312484235379, 0.80901699437494756229, 0.00000000000000000000> <2.11803398874989490253, 2.92705098312484235379, -0.80901699437494756229, 0.00000000000000000000> <2.11803398874989490253, -2.92705098312484235379, 0.80901699437494756229, 0.00000000000000000000> <2.11803398874989490253, -2.92705098312484235379, -0.80901699437494756229, 0.00000000000000000000> <-2.11803398874989490253, 2.92705098312484235379, 0.80901699437494756229, 0.00000000000000000000> <-2.11803398874989490253, 2.92705098312484235379, -0.80901699437494756229, 0.00000000000000000000> <-2.11803398874989490253, -2.92705098312484235379, 0.80901699437494756229, 0.00000000000000000000> <-2.11803398874989490253, -2.92705098312484235379, -0.80901699437494756229, 0.00000000000000000000> <2.92705098312484235379, 0.00000000000000000000, 0.80901699437494756229, 2.11803398874989490253> <2.92705098312484235379, 0.00000000000000000000, 0.80901699437494756229, -2.11803398874989490253> <2.92705098312484235379, 0.00000000000000000000, -0.80901699437494756229, 2.11803398874989490253> <2.92705098312484235379, 0.00000000000000000000, -0.80901699437494756229, -2.11803398874989490253> <-2.92705098312484235379, 0.00000000000000000000, 0.80901699437494756229, 2.11803398874989490253> <-2.92705098312484235379, 0.00000000000000000000, 0.80901699437494756229, -2.11803398874989490253> <-2.92705098312484235379, 0.00000000000000000000, -0.80901699437494756229, 2.11803398874989490253> <-2.92705098312484235379, 0.00000000000000000000, -0.80901699437494756229, -2.11803398874989490253> <2.61803398874989490253, 1.30901699437494745126, 2.11803398874989490253, 0.80901699437494756229> <2.61803398874989490253, 1.30901699437494745126, 2.11803398874989490253, -0.80901699437494756229> <2.61803398874989490253, 1.30901699437494745126, -2.11803398874989490253, 0.80901699437494756229> <2.61803398874989490253, 1.30901699437494745126, -2.11803398874989490253, -0.80901699437494756229> <2.61803398874989490253, -1.30901699437494745126, 2.11803398874989490253, 0.80901699437494756229> <2.61803398874989490253, -1.30901699437494745126, 2.11803398874989490253, -0.80901699437494756229> <2.61803398874989490253, -1.30901699437494745126, -2.11803398874989490253, 0.80901699437494756229> <2.61803398874989490253, -1.30901699437494745126, -2.11803398874989490253, -0.80901699437494756229> <-2.61803398874989490253, 1.30901699437494745126, 2.11803398874989490253, 0.80901699437494756229> <-2.61803398874989490253, 1.30901699437494745126, 2.11803398874989490253, -0.80901699437494756229> <-2.61803398874989490253, 1.30901699437494745126, -2.11803398874989490253, 0.80901699437494756229> <-2.61803398874989490253, 1.30901699437494745126, -2.11803398874989490253, -0.80901699437494756229> <-2.61803398874989490253, -1.30901699437494745126, 2.11803398874989490253, 0.80901699437494756229> <-2.61803398874989490253, -1.30901699437494745126, 2.11803398874989490253, -0.80901699437494756229> <-2.61803398874989490253, -1.30901699437494745126, -2.11803398874989490253, 0.80901699437494756229> <-2.61803398874989490253, -1.30901699437494745126, -2.11803398874989490253, -0.80901699437494756229> <2.61803398874989490253, 2.11803398874989490253, 0.80901699437494756229, 1.30901699437494745126> <2.61803398874989490253, 2.11803398874989490253, 0.80901699437494756229, -1.30901699437494745126> <2.61803398874989490253, 2.11803398874989490253, -0.80901699437494756229, 1.30901699437494745126> <2.61803398874989490253, 2.11803398874989490253, -0.80901699437494756229, -1.30901699437494745126> <2.61803398874989490253, -2.11803398874989490253, 0.80901699437494756229, 1.30901699437494745126> <2.61803398874989490253, -2.11803398874989490253, 0.80901699437494756229, -1.30901699437494745126> <2.61803398874989490253, -2.11803398874989490253, -0.80901699437494756229, 1.30901699437494745126> <2.61803398874989490253, -2.11803398874989490253, -0.80901699437494756229, -1.30901699437494745126> <-2.61803398874989490253, 2.11803398874989490253, 0.80901699437494756229, 1.30901699437494745126> <-2.61803398874989490253, 2.11803398874989490253, 0.80901699437494756229, -1.30901699437494745126> <-2.61803398874989490253, 2.11803398874989490253, -0.80901699437494756229, 1.30901699437494745126> <-2.61803398874989490253, 2.11803398874989490253, -0.80901699437494756229, -1.30901699437494745126> <-2.61803398874989490253, -2.11803398874989490253, 0.80901699437494756229, 1.30901699437494745126> <-2.61803398874989490253, -2.11803398874989490253, 0.80901699437494756229, -1.30901699437494745126> <-2.61803398874989490253, -2.11803398874989490253, -0.80901699437494756229, 1.30901699437494745126> <-2.61803398874989490253, -2.11803398874989490253, -0.80901699437494756229, -1.30901699437494745126> <0.80901699437494756229, 1.30901699437494745126, 2.61803398874989490253, 2.11803398874989490253> <0.80901699437494756229, 1.30901699437494745126, 2.61803398874989490253, -2.11803398874989490253> <0.80901699437494756229, 1.30901699437494745126, -2.61803398874989490253, 2.11803398874989490253> <0.80901699437494756229, 1.30901699437494745126, -2.61803398874989490253, -2.11803398874989490253> <0.80901699437494756229, -1.30901699437494745126, 2.61803398874989490253, 2.11803398874989490253> <0.80901699437494756229, -1.30901699437494745126, 2.61803398874989490253, -2.11803398874989490253> <0.80901699437494756229, -1.30901699437494745126, -2.61803398874989490253, 2.11803398874989490253> <0.80901699437494756229, -1.30901699437494745126, -2.61803398874989490253, -2.11803398874989490253> <-0.80901699437494756229, 1.30901699437494745126, 2.61803398874989490253, 2.11803398874989490253> <-0.80901699437494756229, 1.30901699437494745126, 2.61803398874989490253, -2.11803398874989490253> <-0.80901699437494756229, 1.30901699437494745126, -2.61803398874989490253, 2.11803398874989490253> <-0.80901699437494756229, 1.30901699437494745126, -2.61803398874989490253, -2.11803398874989490253> <-0.80901699437494756229, -1.30901699437494745126, 2.61803398874989490253, 2.11803398874989490253> <-0.80901699437494756229, -1.30901699437494745126, 2.61803398874989490253, -2.11803398874989490253> <-0.80901699437494756229, -1.30901699437494745126, -2.61803398874989490253, 2.11803398874989490253> <-0.80901699437494756229, -1.30901699437494745126, -2.61803398874989490253, -2.11803398874989490253> <0.80901699437494756229, 2.11803398874989490253, 1.30901699437494745126, 2.61803398874989490253> <0.80901699437494756229, 2.11803398874989490253, 1.30901699437494745126, -2.61803398874989490253> <0.80901699437494756229, 2.11803398874989490253, -1.30901699437494745126, 2.61803398874989490253> <0.80901699437494756229, 2.11803398874989490253, -1.30901699437494745126, -2.61803398874989490253> <0.80901699437494756229, -2.11803398874989490253, 1.30901699437494745126, 2.61803398874989490253> <0.80901699437494756229, -2.11803398874989490253, 1.30901699437494745126, -2.61803398874989490253> <0.80901699437494756229, -2.11803398874989490253, -1.30901699437494745126, 2.61803398874989490253> <0.80901699437494756229, -2.11803398874989490253, -1.30901699437494745126, -2.61803398874989490253> <-0.80901699437494756229, 2.11803398874989490253, 1.30901699437494745126, 2.61803398874989490253> <-0.80901699437494756229, 2.11803398874989490253, 1.30901699437494745126, -2.61803398874989490253> <-0.80901699437494756229, 2.11803398874989490253, -1.30901699437494745126, 2.61803398874989490253> <-0.80901699437494756229, 2.11803398874989490253, -1.30901699437494745126, -2.61803398874989490253> <-0.80901699437494756229, -2.11803398874989490253, 1.30901699437494745126, 2.61803398874989490253> <-0.80901699437494756229, -2.11803398874989490253, 1.30901699437494745126, -2.61803398874989490253> <-0.80901699437494756229, -2.11803398874989490253, -1.30901699437494745126, 2.61803398874989490253> <-0.80901699437494756229, -2.11803398874989490253, -1.30901699437494745126, -2.61803398874989490253> <0.80901699437494756229, 2.61803398874989490253, 2.11803398874989490253, 1.30901699437494745126> <0.80901699437494756229, 2.61803398874989490253, 2.11803398874989490253, -1.30901699437494745126> <0.80901699437494756229, 2.61803398874989490253, -2.11803398874989490253, 1.30901699437494745126> <0.80901699437494756229, 2.61803398874989490253, -2.11803398874989490253, -1.30901699437494745126> <0.80901699437494756229, -2.61803398874989490253, 2.11803398874989490253, 1.30901699437494745126> <0.80901699437494756229, -2.61803398874989490253, 2.11803398874989490253, -1.30901699437494745126> <0.80901699437494756229, -2.61803398874989490253, -2.11803398874989490253, 1.30901699437494745126> <0.80901699437494756229, -2.61803398874989490253, -2.11803398874989490253, -1.30901699437494745126> <-0.80901699437494756229, 2.61803398874989490253, 2.11803398874989490253, 1.30901699437494745126> <-0.80901699437494756229, 2.61803398874989490253, 2.11803398874989490253, -1.30901699437494745126> <-0.80901699437494756229, 2.61803398874989490253, -2.11803398874989490253, 1.30901699437494745126> <-0.80901699437494756229, 2.61803398874989490253, -2.11803398874989490253, -1.30901699437494745126> <-0.80901699437494756229, -2.61803398874989490253, 2.11803398874989490253, 1.30901699437494745126> <-0.80901699437494756229, -2.61803398874989490253, 2.11803398874989490253, -1.30901699437494745126> <-0.80901699437494756229, -2.61803398874989490253, -2.11803398874989490253, 1.30901699437494745126> <-0.80901699437494756229, -2.61803398874989490253, -2.11803398874989490253, -1.30901699437494745126> <1.30901699437494745126, 0.80901699437494756229, 2.11803398874989490253, 2.61803398874989490253> <1.30901699437494745126, 0.80901699437494756229, 2.11803398874989490253, -2.61803398874989490253> <1.30901699437494745126, 0.80901699437494756229, -2.11803398874989490253, 2.61803398874989490253> <1.30901699437494745126, 0.80901699437494756229, -2.11803398874989490253, -2.61803398874989490253> <1.30901699437494745126, -0.80901699437494756229, 2.11803398874989490253, 2.61803398874989490253> <1.30901699437494745126, -0.80901699437494756229, 2.11803398874989490253, -2.61803398874989490253> <1.30901699437494745126, -0.80901699437494756229, -2.11803398874989490253, 2.61803398874989490253> <1.30901699437494745126, -0.80901699437494756229, -2.11803398874989490253, -2.61803398874989490253> <-1.30901699437494745126, 0.80901699437494756229, 2.11803398874989490253, 2.61803398874989490253> <-1.30901699437494745126, 0.80901699437494756229, 2.11803398874989490253, -2.61803398874989490253> <-1.30901699437494745126, 0.80901699437494756229, -2.11803398874989490253, 2.61803398874989490253> <-1.30901699437494745126, 0.80901699437494756229, -2.11803398874989490253, -2.61803398874989490253> <-1.30901699437494745126, -0.80901699437494756229, 2.11803398874989490253, 2.61803398874989490253> <-1.30901699437494745126, -0.80901699437494756229, 2.11803398874989490253, -2.61803398874989490253> <-1.30901699437494745126, -0.80901699437494756229, -2.11803398874989490253, 2.61803398874989490253> <-1.30901699437494745126, -0.80901699437494756229, -2.11803398874989490253, -2.61803398874989490253> <1.30901699437494745126, 2.11803398874989490253, 2.61803398874989490253, 0.80901699437494756229> <1.30901699437494745126, 2.11803398874989490253, 2.61803398874989490253, -0.80901699437494756229> <1.30901699437494745126, 2.11803398874989490253, -2.61803398874989490253, 0.80901699437494756229> <1.30901699437494745126, 2.11803398874989490253, -2.61803398874989490253, -0.80901699437494756229> <1.30901699437494745126, -2.11803398874989490253, 2.61803398874989490253, 0.80901699437494756229> <1.30901699437494745126, -2.11803398874989490253, 2.61803398874989490253, -0.80901699437494756229> <1.30901699437494745126, -2.11803398874989490253, -2.61803398874989490253, 0.80901699437494756229> <1.30901699437494745126, -2.11803398874989490253, -2.61803398874989490253, -0.80901699437494756229> <-1.30901699437494745126, 2.11803398874989490253, 2.61803398874989490253, 0.80901699437494756229> <-1.30901699437494745126, 2.11803398874989490253, 2.61803398874989490253, -0.80901699437494756229> <-1.30901699437494745126, 2.11803398874989490253, -2.61803398874989490253, 0.80901699437494756229> <-1.30901699437494745126, 2.11803398874989490253, -2.61803398874989490253, -0.80901699437494756229> <-1.30901699437494745126, -2.11803398874989490253, 2.61803398874989490253, 0.80901699437494756229> <-1.30901699437494745126, -2.11803398874989490253, 2.61803398874989490253, -0.80901699437494756229> <-1.30901699437494745126, -2.11803398874989490253, -2.61803398874989490253, 0.80901699437494756229> <-1.30901699437494745126, -2.11803398874989490253, -2.61803398874989490253, -0.80901699437494756229> <1.30901699437494745126, 2.61803398874989490253, 0.80901699437494756229, 2.11803398874989490253> <1.30901699437494745126, 2.61803398874989490253, 0.80901699437494756229, -2.11803398874989490253> <1.30901699437494745126, 2.61803398874989490253, -0.80901699437494756229, 2.11803398874989490253> <1.30901699437494745126, 2.61803398874989490253, -0.80901699437494756229, -2.11803398874989490253> <1.30901699437494745126, -2.61803398874989490253, 0.80901699437494756229, 2.11803398874989490253> <1.30901699437494745126, -2.61803398874989490253, 0.80901699437494756229, -2.11803398874989490253> <1.30901699437494745126, -2.61803398874989490253, -0.80901699437494756229, 2.11803398874989490253> <1.30901699437494745126, -2.61803398874989490253, -0.80901699437494756229, -2.11803398874989490253> <-1.30901699437494745126, 2.61803398874989490253, 0.80901699437494756229, 2.11803398874989490253> <-1.30901699437494745126, 2.61803398874989490253, 0.80901699437494756229, -2.11803398874989490253> <-1.30901699437494745126, 2.61803398874989490253, -0.80901699437494756229, 2.11803398874989490253> <-1.30901699437494745126, 2.61803398874989490253, -0.80901699437494756229, -2.11803398874989490253> <-1.30901699437494745126, -2.61803398874989490253, 0.80901699437494756229, 2.11803398874989490253> <-1.30901699437494745126, -2.61803398874989490253, 0.80901699437494756229, -2.11803398874989490253> <-1.30901699437494745126, -2.61803398874989490253, -0.80901699437494756229, 2.11803398874989490253> <-1.30901699437494745126, -2.61803398874989490253, -0.80901699437494756229, -2.11803398874989490253> <2.11803398874989490253, 0.80901699437494756229, 2.61803398874989490253, 1.30901699437494745126> <2.11803398874989490253, 0.80901699437494756229, 2.61803398874989490253, -1.30901699437494745126> <2.11803398874989490253, 0.80901699437494756229, -2.61803398874989490253, 1.30901699437494745126> <2.11803398874989490253, 0.80901699437494756229, -2.61803398874989490253, -1.30901699437494745126> <2.11803398874989490253, -0.80901699437494756229, 2.61803398874989490253, 1.30901699437494745126> <2.11803398874989490253, -0.80901699437494756229, 2.61803398874989490253, -1.30901699437494745126> <2.11803398874989490253, -0.80901699437494756229, -2.61803398874989490253, 1.30901699437494745126> <2.11803398874989490253, -0.80901699437494756229, -2.61803398874989490253, -1.30901699437494745126> <-2.11803398874989490253, 0.80901699437494756229, 2.61803398874989490253, 1.30901699437494745126> <-2.11803398874989490253, 0.80901699437494756229, 2.61803398874989490253, -1.30901699437494745126> <-2.11803398874989490253, 0.80901699437494756229, -2.61803398874989490253, 1.30901699437494745126> <-2.11803398874989490253, 0.80901699437494756229, -2.61803398874989490253, -1.30901699437494745126> <-2.11803398874989490253, -0.80901699437494756229, 2.61803398874989490253, 1.30901699437494745126> <-2.11803398874989490253, -0.80901699437494756229, 2.61803398874989490253, -1.30901699437494745126> <-2.11803398874989490253, -0.80901699437494756229, -2.61803398874989490253, 1.30901699437494745126> <-2.11803398874989490253, -0.80901699437494756229, -2.61803398874989490253, -1.30901699437494745126> <2.11803398874989490253, 1.30901699437494745126, 0.80901699437494756229, 2.61803398874989490253> <2.11803398874989490253, 1.30901699437494745126, 0.80901699437494756229, -2.61803398874989490253> <2.11803398874989490253, 1.30901699437494745126, -0.80901699437494756229, 2.61803398874989490253> <2.11803398874989490253, 1.30901699437494745126, -0.80901699437494756229, -2.61803398874989490253> <2.11803398874989490253, -1.30901699437494745126, 0.80901699437494756229, 2.61803398874989490253> <2.11803398874989490253, -1.30901699437494745126, 0.80901699437494756229, -2.61803398874989490253> <2.11803398874989490253, -1.30901699437494745126, -0.80901699437494756229, 2.61803398874989490253> <2.11803398874989490253, -1.30901699437494745126, -0.80901699437494756229, -2.61803398874989490253> <-2.11803398874989490253, 1.30901699437494745126, 0.80901699437494756229, 2.61803398874989490253> <-2.11803398874989490253, 1.30901699437494745126, 0.80901699437494756229, -2.61803398874989490253> <-2.11803398874989490253, 1.30901699437494745126, -0.80901699437494756229, 2.61803398874989490253> <-2.11803398874989490253, 1.30901699437494745126, -0.80901699437494756229, -2.61803398874989490253> <-2.11803398874989490253, -1.30901699437494745126, 0.80901699437494756229, 2.61803398874989490253> <-2.11803398874989490253, -1.30901699437494745126, 0.80901699437494756229, -2.61803398874989490253> <-2.11803398874989490253, -1.30901699437494745126, -0.80901699437494756229, 2.61803398874989490253> <-2.11803398874989490253, -1.30901699437494745126, -0.80901699437494756229, -2.61803398874989490253> <2.11803398874989490253, 2.61803398874989490253, 1.30901699437494745126, 0.80901699437494756229> <2.11803398874989490253, 2.61803398874989490253, 1.30901699437494745126, -0.80901699437494756229> <2.11803398874989490253, 2.61803398874989490253, -1.30901699437494745126, 0.80901699437494756229> <2.11803398874989490253, 2.61803398874989490253, -1.30901699437494745126, -0.80901699437494756229> <2.11803398874989490253, -2.61803398874989490253, 1.30901699437494745126, 0.80901699437494756229> <2.11803398874989490253, -2.61803398874989490253, 1.30901699437494745126, -0.80901699437494756229> <2.11803398874989490253, -2.61803398874989490253, -1.30901699437494745126, 0.80901699437494756229> <2.11803398874989490253, -2.61803398874989490253, -1.30901699437494745126, -0.80901699437494756229> <-2.11803398874989490253, 2.61803398874989490253, 1.30901699437494745126, 0.80901699437494756229> <-2.11803398874989490253, 2.61803398874989490253, 1.30901699437494745126, -0.80901699437494756229> <-2.11803398874989490253, 2.61803398874989490253, -1.30901699437494745126, 0.80901699437494756229> <-2.11803398874989490253, 2.61803398874989490253, -1.30901699437494745126, -0.80901699437494756229> <-2.11803398874989490253, -2.61803398874989490253, 1.30901699437494745126, 0.80901699437494756229> <-2.11803398874989490253, -2.61803398874989490253, 1.30901699437494745126, -0.80901699437494756229> <-2.11803398874989490253, -2.61803398874989490253, -1.30901699437494745126, 0.80901699437494756229> <-2.11803398874989490253, -2.61803398874989490253, -1.30901699437494745126, -0.80901699437494756229> <2.61803398874989490253, 0.80901699437494756229, 1.30901699437494745126, 2.11803398874989490253> <2.61803398874989490253, 0.80901699437494756229, 1.30901699437494745126, -2.11803398874989490253> <2.61803398874989490253, 0.80901699437494756229, -1.30901699437494745126, 2.11803398874989490253> <2.61803398874989490253, 0.80901699437494756229, -1.30901699437494745126, -2.11803398874989490253> <2.61803398874989490253, -0.80901699437494756229, 1.30901699437494745126, 2.11803398874989490253> <2.61803398874989490253, -0.80901699437494756229, 1.30901699437494745126, -2.11803398874989490253> <2.61803398874989490253, -0.80901699437494756229, -1.30901699437494745126, 2.11803398874989490253> <2.61803398874989490253, -0.80901699437494756229, -1.30901699437494745126, -2.11803398874989490253> <-2.61803398874989490253, 0.80901699437494756229, 1.30901699437494745126, 2.11803398874989490253> <-2.61803398874989490253, 0.80901699437494756229, 1.30901699437494745126, -2.11803398874989490253> <-2.61803398874989490253, 0.80901699437494756229, -1.30901699437494745126, 2.11803398874989490253> <-2.61803398874989490253, 0.80901699437494756229, -1.30901699437494745126, -2.11803398874989490253> <-2.61803398874989490253, -0.80901699437494756229, 1.30901699437494745126, 2.11803398874989490253> <-2.61803398874989490253, -0.80901699437494756229, 1.30901699437494745126, -2.11803398874989490253> <-2.61803398874989490253, -0.80901699437494756229, -1.30901699437494745126, 2.11803398874989490253> <-2.61803398874989490253, -0.80901699437494756229, -1.30901699437494745126, -2.11803398874989490253>

Does that help?

by **benb** » Mon Jan 27, 2014 5:32 pm

@quickfur: Yes, the raw coordinates are for easy-making. I've been playing around with what I've started to call the "starfield" based on its appearance: the vertices as indicated by small multicolored tesseracts in the 4D manifold without any visual indicators of the edges or faces (think constellation in the night sky). Sometimes easily identifiable patterns seem salient; at other times, not so much. I'm posting the code here for those who wish to load and/or modify it for visualizing via the Double Rainbow Display or McIntosh's earlier 3D retina configuration.

Code: Select all: "library" include block4 [.25 .25 .25 .25] scale [ 10.47213596 25.47213596 0 -3 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 4.527864044 0 -3 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 25.47213596 0 -3 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 4.527864044 0 -3 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 0 15 10.47213596 7.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 0 15 10.47213596 -13.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 0 15 -10.47213596 7.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 0 15 -10.47213596 -13.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 0 25.47213596 0 7.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 0 25.47213596 0 -13.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 0 4.527864044 0 7.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 0 4.527864044 0 -13.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 0 25.47213596 10.47213596 -3 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 0 25.47213596 -10.47213596 -3 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 0 4.527864044 10.47213596 -3 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 0 4.527864044 -10.47213596 -3 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 15 0 7.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 15 0 -13.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 15 0 7.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 15 0 -13.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 15 10.47213596 -3 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 15 -10.47213596 -3 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 15 10.47213596 -3 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 15 -10.47213596 -3 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 20.23606798 5.236067976 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 20.23606798 5.236067976 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 20.23606798 -5.236067976 2.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 20.23606798 -5.236067976 -8.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 9.763932024 5.236067976 2.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 9.763932024 5.236067976 -8.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 9.763932024 -5.236067976 2.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 9.763932024 -5.236067976 -8.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 20.23606798 5.236067976 2.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 20.23606798 5.236067976 -8.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 20.23606798 -5.236067976 2.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 20.23606798 -5.236067976 -8.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 9.763932024 5.236067976 2.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 9.763932024 5.236067976 -8.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 9.763932024 -5.236067976 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 9.763932024 -5.236067976 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 20.23606798 5.236067976 8.708203932 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 20.23606798 5.236067976 -14.70820393 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 20.23606798 -5.236067976 8.708203932 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 20.23606798 -5.236067976 -14.70820393 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 9.763932024 5.236067976 8.708203932 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 9.763932024 5.236067976 -14.70820393 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 9.763932024 -5.236067976 8.708203932 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 9.763932024 -5.236067976 -14.70820393 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 20.23606798 5.236067976 8.708203932 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 20.23606798 5.236067976 -14.70820393 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 20.23606798 -5.236067976 8.708203932 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 20.23606798 -5.236067976 -14.70820393 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 9.763932024 5.236067976 8.708203932 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 9.763932024 5.236067976 -14.70820393 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 9.763932024 -5.236067976 8.708203932 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 9.763932024 -5.236067976 -14.70820393 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 20.23606798 11.70820393 2.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 20.23606798 11.70820393 -8.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 20.23606798 -11.70820393 2.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 20.23606798 -11.70820393 -8.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 9.763932024 11.70820393 2.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 9.763932024 11.70820393 -8.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 9.763932024 -11.70820393 2.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 9.763932024 -11.70820393 -8.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 20.23606798 11.70820393 2.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 20.23606798 11.70820393 -8.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 20.23606798 -11.70820393 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 20.23606798 -11.70820393 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 9.763932024 11.70820393 2.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 9.763932024 11.70820393 -8.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 9.763932024 -11.70820393 2.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 9.763932024 -11.70820393 -8.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 26.70820393 5.236067976 2.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 26.70820393 5.236067976 -8.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 26.70820393 -5.236067976 2.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 26.70820393 -5.236067976 -8.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 3.291796068 5.236067976 2.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 3.291796068 5.236067976 -8.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 3.291796068 -5.236067976 2.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 3.291796068 -5.236067976 -8.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 26.70820393 5.236067976 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 26.70820393 5.236067976 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 26.70820393 -5.236067976 2.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 26.70820393 -5.236067976 -8.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 3.291796068 5.236067976 2.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 3.291796068 5.236067976 -8.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 3.291796068 -5.236067976 2.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 3.291796068 -5.236067976 -8.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 23.47213596 8.472135956 -1 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 23.47213596 8.472135956 -5 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 23.47213596 -8.472135956 -1 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 23.47213596 -8.472135956 -5 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 6.527864044 8.472135956 -1 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 6.527864044 8.472135956 -5 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 6.527864044 -8.472135956 -1 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 6.527864044 -8.472135956 -5 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 23.47213596 8.472135956 -1 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 23.47213596 8.472135956 -5 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 23.47213596 -8.472135956 -1 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 23.47213596 -8.472135956 -5 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 6.527864044 8.472135956 -1 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 6.527864044 8.472135956 -5 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 6.527864044 -8.472135956 -1 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 6.527864044 -8.472135956 -5 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 2 23.47213596 8.472135956 5.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 2 23.47213596 8.472135956 -11.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 2 23.47213596 -8.472135956 5.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 2 23.47213596 -8.472135956 -11.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 2 6.527864044 8.472135956 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 2 6.527864044 8.472135956 -11.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 2 6.527864044 -8.472135956 5.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 2 6.527864044 -8.472135956 -11.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -2 23.47213596 8.472135956 5.472135956 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -2 23.47213596 8.472135956 -11.47213596 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -2 23.47213596 -8.472135956 5.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -2 23.47213596 -8.472135956 -11.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -2 6.527864044 8.472135956 5.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -2 6.527864044 8.472135956 -11.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -2 6.527864044 -8.472135956 5.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -2 6.527864044 -8.472135956 -11.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 17 8.472135956 5.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 17 8.472135956 -11.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 17 -8.472135956 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 17 -8.472135956 -11.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 13 8.472135956 5.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 13 8.472135956 -11.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 13 -8.472135956 5.472135956 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 13 -8.472135956 -11.47213596 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 17 8.472135956 5.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 17 8.472135956 -11.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 17 -8.472135956 5.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 17 -8.472135956 -11.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 13 8.472135956 5.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 13 8.472135956 -11.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 13 -8.472135956 5.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 13 -8.472135956 -11.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 23.47213596 2 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 23.47213596 2 -11.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 23.47213596 -2 5.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 23.47213596 -2 -11.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 6.527864044 2 5.472135956 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 6.527864044 2 -11.47213596 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 6.527864044 -2 5.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 6.527864044 -2 -11.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 23.47213596 2 5.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 23.47213596 2 -11.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 23.47213596 -2 5.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 23.47213596 -2 -11.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 6.527864044 2 5.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 6.527864044 2 -11.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 6.527864044 -2 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 6.527864044 -2 -11.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 18.23606798 3.236067976 0.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 18.23606798 3.236067976 -6.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 18.23606798 -3.236067976 0.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 18.23606798 -3.236067976 -6.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 11.76393202 3.236067976 0.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 11.76393202 3.236067976 -6.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 11.76393202 -3.236067976 0.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 11.76393202 -3.236067976 -6.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 18.23606798 3.236067976 0.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 18.23606798 3.236067976 -6.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 18.23606798 -3.236067976 0.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 18.23606798 -3.236067976 -6.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 11.76393202 3.236067976 0.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 11.76393202 3.236067976 -6.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 11.76393202 -3.236067976 0.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 11.76393202 -3.236067976 -6.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 18.23606798 3.236067976 10.70820393 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 18.23606798 3.236067976 -16.70820393 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 18.23606798 -3.236067976 10.70820393 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 18.23606798 -3.236067976 -16.70820393 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 11.76393202 3.236067976 10.70820393 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 11.76393202 3.236067976 -16.70820393 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 11.76393202 -3.236067976 10.70820393 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 11.76393202 -3.236067976 -16.70820393 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 18.23606798 3.236067976 10.70820393 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 18.23606798 3.236067976 -16.70820393 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 18.23606798 -3.236067976 10.70820393 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 18.23606798 -3.236067976 -16.70820393 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 11.76393202 3.236067976 10.70820393 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 11.76393202 3.236067976 -16.70820393 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 11.76393202 -3.236067976 10.70820393 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 11.76393202 -3.236067976 -16.70820393 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 18.23606798 13.70820393 0.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 18.23606798 13.70820393 -6.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 18.23606798 -13.70820393 0.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 18.23606798 -13.70820393 -6.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 11.76393202 13.70820393 0.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 11.76393202 13.70820393 -6.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 11.76393202 -13.70820393 0.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 11.76393202 -13.70820393 -6.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 18.23606798 13.70820393 0.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 18.23606798 13.70820393 -6.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 18.23606798 -13.70820393 0.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 18.23606798 -13.70820393 -6.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 11.76393202 13.70820393 0.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 11.76393202 13.70820393 -6.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 11.76393202 -13.70820393 0.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 11.76393202 -13.70820393 -6.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 28.70820393 3.236067976 0.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 28.70820393 3.236067976 -6.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 28.70820393 -3.236067976 0.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 28.70820393 -3.236067976 -6.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 1.291796068 3.236067976 0.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 1.291796068 3.236067976 -6.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 1.291796068 -3.236067976 0.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 1.291796068 -3.236067976 -6.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 28.70820393 3.236067976 0.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 28.70820393 3.236067976 -6.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 28.70820393 -3.236067976 0.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 28.70820393 -3.236067976 -6.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 1.291796068 3.236067976 0.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 1.291796068 3.236067976 -6.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 1.291796068 -3.236067976 0.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 1.291796068 -3.236067976 -6.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 17 5.236067976 -3 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 17 -5.236067976 -3 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 13 5.236067976 -3 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 13 -5.236067976 -3 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 17 5.236067976 -3 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 17 -5.236067976 -3 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 13 5.236067976 -3 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 13 -5.236067976 -3 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 20.23606798 0 -1 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 20.23606798 0 -5 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 9.763932024 0 -1 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 9.763932024 0 -5 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 20.23606798 0 -1 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 20.23606798 0 -5 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 9.763932024 0 -1 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 9.763932024 0 -5 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 0 17 13.70820393 2.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 0 17 13.70820393 -8.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 0 17 -13.70820393 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 0 17 -13.70820393 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 0 13 13.70820393 2.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 0 13 13.70820393 -8.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 0 13 -13.70820393 2.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 0 13 -13.70820393 -8.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 0 20.23606798 2 10.70820393 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 0 20.23606798 2 -16.70820393 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 0 20.23606798 -2 10.70820393 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 0 20.23606798 -2 -16.70820393 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 0 9.763932024 2 10.70820393 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 0 9.763932024 2 -16.70820393 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 0 9.763932024 -2 10.70820393 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 0 9.763932024 -2 -16.70820393 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 0 28.70820393 5.236067976 -1 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 0 28.70820393 5.236067976 -5 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 0 28.70820393 -5.236067976 -1 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 0 28.70820393 -5.236067976 -5 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 0 1.291796068 5.236067976 -1 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 0 1.291796068 5.236067976 -5 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 0 1.291796068 -5.236067976 -1 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 0 1.291796068 -5.236067976 -5 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 2 15 5.236067976 10.70820393 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 2 15 5.236067976 -16.70820393 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 2 15 -5.236067976 10.70820393 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 2 15 -5.236067976 -16.70820393 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -2 15 5.236067976 10.70820393 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -2 15 5.236067976 -16.70820393 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -2 15 -5.236067976 10.70820393 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -2 15 -5.236067976 -16.70820393 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 2 20.23606798 13.70820393 -3 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 2 20.23606798 -13.70820393 -3 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 2 9.763932024 13.70820393 -3 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 2 9.763932024 -13.70820393 -3 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -2 20.23606798 13.70820393 -3 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -2 20.23606798 -13.70820393 -3 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -2 9.763932024 13.70820393 -3 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -2 9.763932024 -13.70820393 -3 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 2 28.70820393 0 2.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 2 28.70820393 0 -8.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 2 1.291796068 0 2.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 2 1.291796068 0 -8.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -2 28.70820393 0 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -2 28.70820393 0 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -2 1.291796068 0 2.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -2 1.291796068 0 -8.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 15 13.70820393 -1 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 15 13.70820393 -5 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 15 -13.70820393 -1 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 15 -13.70820393 -5 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 15 13.70820393 -1 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 15 13.70820393 -5 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 15 -13.70820393 -1 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 15 -13.70820393 -5 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 17 0 10.70820393 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 17 0 -16.70820393 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 13 0 10.70820393 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 13 0 -16.70820393 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 17 0 10.70820393 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 17 0 -16.70820393 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 13 0 10.70820393 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 13 0 -16.70820393 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 28.70820393 2 -3 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 28.70820393 -2 -3 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 1.291796068 2 -3 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 1.291796068 -2 -3 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 28.70820393 2 -3 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 28.70820393 -2 -3 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 1.291796068 2 -3 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 1.291796068 -2 -3 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 15 2 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 15 2 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 15 -2 2.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 13.70820393 15 -2 -8.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 15 2 2.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 15 2 -8.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 15 -2 2.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -13.70820393 15 -2 -8.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 18.23606798 8.472135956 -3 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 18.23606798 -8.472135956 -3 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 11.76393202 8.472135956 -3 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 11.76393202 -8.472135956 -3 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 18.23606798 8.472135956 -3 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 18.23606798 -8.472135956 -3 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 11.76393202 8.472135956 -3 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 11.76393202 -8.472135956 -3 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 23.47213596 0 0.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 23.47213596 0 -6.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 6.527864044 0 0.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 6.527864044 0 -6.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 23.47213596 0 0.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 23.47213596 0 -6.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 6.527864044 0 0.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 6.527864044 0 -6.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 0 18.23606798 11.70820393 5.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 0 18.23606798 11.70820393 -11.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 0 18.23606798 -11.70820393 5.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 0 18.23606798 -11.70820393 -11.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 0 11.76393202 11.70820393 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 0 11.76393202 11.70820393 -11.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 0 11.76393202 -11.70820393 5.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 0 11.76393202 -11.70820393 -11.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 0 23.47213596 3.236067976 8.708203932 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 0 23.47213596 3.236067976 -14.70820393 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 0 23.47213596 -3.236067976 8.708203932 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 0 23.47213596 -3.236067976 -14.70820393 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 0 6.527864044 3.236067976 8.708203932 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 0 6.527864044 3.236067976 -14.70820393 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 0 6.527864044 -3.236067976 8.708203932 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 0 6.527864044 -3.236067976 -14.70820393 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 0 26.70820393 8.472135956 0.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 0 26.70820393 8.472135956 -6.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 0 26.70820393 -8.472135956 0.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 0 26.70820393 -8.472135956 -6.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 0 3.291796068 8.472135956 0.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 0 3.291796068 8.472135956 -6.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 0 3.291796068 -8.472135956 0.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 0 3.291796068 -8.472135956 -6.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 15 8.472135956 8.708203932 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 15 8.472135956 -14.70820393 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 15 -8.472135956 8.708203932 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 15 -8.472135956 -14.70820393 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 15 8.472135956 8.708203932 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 15 8.472135956 -14.70820393 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 15 -8.472135956 8.708203932 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 15 -8.472135956 -14.70820393 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 23.47213596 11.70820393 -3 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 23.47213596 -11.70820393 -3 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 6.527864044 11.70820393 -3 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 6.527864044 -11.70820393 -3 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 23.47213596 11.70820393 -3 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 23.47213596 -11.70820393 -3 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 6.527864044 11.70820393 -3 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 6.527864044 -11.70820393 -3 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 26.70820393 0 5.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 26.70820393 0 -11.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 3.291796068 0 5.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 3.291796068 0 -11.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 26.70820393 0 5.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 26.70820393 0 -11.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 3.291796068 0 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 3.291796068 0 -11.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 15 11.70820393 0.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 15 11.70820393 -6.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 15 -11.70820393 0.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 15 -11.70820393 -6.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 15 11.70820393 0.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 15 11.70820393 -6.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 15 -11.70820393 0.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 15 -11.70820393 -6.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 18.23606798 0 8.708203932 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 18.23606798 0 -14.70820393 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 11.76393202 0 8.708203932 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 11.76393202 0 -14.70820393 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 18.23606798 0 8.708203932 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 18.23606798 0 -14.70820393 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 11.76393202 0 8.708203932 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 11.76393202 0 -14.70820393 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 26.70820393 3.236067976 -3 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 26.70820393 -3.236067976 -3 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 3.291796068 3.236067976 -3 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 3.291796068 -3.236067976 -3 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 26.70820393 3.236067976 -3 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 26.70820393 -3.236067976 -3 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 3.291796068 3.236067976 -3 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 3.291796068 -3.236067976 -3 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 15 3.236067976 5.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 15 3.236067976 -11.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 15 -3.236067976 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 11.70820393 15 -3.236067976 -11.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 15 3.236067976 5.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 15 3.236067976 -11.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 15 -3.236067976 5.472135956 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -11.70820393 15 -3.236067976 -11.47213596 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 20.23606798 8.472135956 0.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 20.23606798 8.472135956 -6.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 20.23606798 -8.472135956 0.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 20.23606798 -8.472135956 -6.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 9.763932024 8.472135956 0.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 9.763932024 8.472135956 -6.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 9.763932024 -8.472135956 0.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 9.763932024 -8.472135956 -6.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 20.23606798 8.472135956 0.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 20.23606798 8.472135956 -6.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 20.23606798 -8.472135956 0.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 20.23606798 -8.472135956 -6.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 9.763932024 8.472135956 0.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 9.763932024 8.472135956 -6.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 9.763932024 -8.472135956 0.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 9.763932024 -8.472135956 -6.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 23.47213596 3.236067976 2.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 23.47213596 3.236067976 -8.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 23.47213596 -3.236067976 2.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 23.47213596 -3.236067976 -8.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 6.527864044 3.236067976 2.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 6.527864044 3.236067976 -8.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 6.527864044 -3.236067976 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 6.527864044 -3.236067976 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 23.47213596 3.236067976 2.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 23.47213596 3.236067976 -8.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 23.47213596 -3.236067976 2.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 23.47213596 -3.236067976 -8.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 6.527864044 3.236067976 2.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 6.527864044 3.236067976 -8.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 6.527864044 -3.236067976 2.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 6.527864044 -3.236067976 -8.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 20.23606798 10.47213596 5.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 20.23606798 10.47213596 -11.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 20.23606798 -10.47213596 5.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 20.23606798 -10.47213596 -11.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 9.763932024 10.47213596 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 9.763932024 10.47213596 -11.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 9.763932024 -10.47213596 5.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 9.763932024 -10.47213596 -11.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 20.23606798 10.47213596 5.472135956 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 20.23606798 10.47213596 -11.47213596 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 20.23606798 -10.47213596 5.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 20.23606798 -10.47213596 -11.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 9.763932024 10.47213596 5.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 9.763932024 10.47213596 -11.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 9.763932024 -10.47213596 5.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 9.763932024 -10.47213596 -11.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 23.47213596 5.236067976 7.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 23.47213596 5.236067976 -13.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 23.47213596 -5.236067976 7.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 23.47213596 -5.236067976 -13.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 6.527864044 5.236067976 7.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 6.527864044 5.236067976 -13.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 6.527864044 -5.236067976 7.472135956 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 6.527864044 -5.236067976 -13.47213596 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 23.47213596 5.236067976 7.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 23.47213596 5.236067976 -13.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 23.47213596 -5.236067976 7.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 23.47213596 -5.236067976 -13.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 6.527864044 5.236067976 7.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 6.527864044 5.236067976 -13.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 6.527864044 -5.236067976 7.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 6.527864044 -5.236067976 -13.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 25.47213596 8.472135956 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 25.47213596 8.472135956 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 25.47213596 -8.472135956 2.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 25.47213596 -8.472135956 -8.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 4.527864044 8.472135956 2.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 4.527864044 8.472135956 -8.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 4.527864044 -8.472135956 2.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 3.236067976 4.527864044 -8.472135956 -8.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 25.47213596 8.472135956 2.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 25.47213596 8.472135956 -8.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 25.47213596 -8.472135956 2.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 25.47213596 -8.472135956 -8.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 4.527864044 8.472135956 2.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 4.527864044 8.472135956 -8.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 4.527864044 -8.472135956 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -3.236067976 4.527864044 -8.472135956 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 18.23606798 8.472135956 7.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 18.23606798 8.472135956 -13.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 18.23606798 -8.472135956 7.472135956 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 18.23606798 -8.472135956 -13.47213596 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 11.76393202 8.472135956 7.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 11.76393202 8.472135956 -13.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 11.76393202 -8.472135956 7.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 11.76393202 -8.472135956 -13.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 18.23606798 8.472135956 7.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 18.23606798 8.472135956 -13.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 18.23606798 -8.472135956 7.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 18.23606798 -8.472135956 -13.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 11.76393202 8.472135956 7.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 11.76393202 8.472135956 -13.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 11.76393202 -8.472135956 7.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 11.76393202 -8.472135956 -13.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 23.47213596 10.47213596 0.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 23.47213596 10.47213596 -6.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 23.47213596 -10.47213596 0.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 23.47213596 -10.47213596 -6.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 6.527864044 10.47213596 0.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 6.527864044 10.47213596 -6.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 6.527864044 -10.47213596 0.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 6.527864044 -10.47213596 -6.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 23.47213596 10.47213596 0.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 23.47213596 10.47213596 -6.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 23.47213596 -10.47213596 0.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 23.47213596 -10.47213596 -6.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 6.527864044 10.47213596 0.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 6.527864044 10.47213596 -6.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 6.527864044 -10.47213596 0.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 6.527864044 -10.47213596 -6.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 25.47213596 3.236067976 5.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 25.47213596 3.236067976 -11.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 25.47213596 -3.236067976 5.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 25.47213596 -3.236067976 -11.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 4.527864044 3.236067976 5.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 4.527864044 3.236067976 -11.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 4.527864044 -3.236067976 5.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 5.236067976 4.527864044 -3.236067976 -11.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 25.47213596 3.236067976 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 25.47213596 3.236067976 -11.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 25.47213596 -3.236067976 5.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 25.47213596 -3.236067976 -11.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 4.527864044 3.236067976 5.472135956 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 4.527864044 3.236067976 -11.47213596 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 4.527864044 -3.236067976 5.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -5.236067976 4.527864044 -3.236067976 -11.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 18.23606798 10.47213596 2.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 18.23606798 10.47213596 -8.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 18.23606798 -10.47213596 2.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 18.23606798 -10.47213596 -8.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 11.76393202 10.47213596 2.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 11.76393202 10.47213596 -8.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 11.76393202 -10.47213596 2.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 11.76393202 -10.47213596 -8.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 18.23606798 10.47213596 2.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 18.23606798 10.47213596 -8.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 18.23606798 -10.47213596 2.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 18.23606798 -10.47213596 -8.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 11.76393202 10.47213596 2.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 11.76393202 10.47213596 -8.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 11.76393202 -10.47213596 2.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 11.76393202 -10.47213596 -8.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 20.23606798 3.236067976 7.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 20.23606798 3.236067976 -13.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 20.23606798 -3.236067976 7.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 20.23606798 -3.236067976 -13.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 9.763932024 3.236067976 7.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 9.763932024 3.236067976 -13.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 9.763932024 -3.236067976 7.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 9.763932024 -3.236067976 -13.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 20.23606798 3.236067976 7.472135956 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 20.23606798 3.236067976 -13.47213596 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 20.23606798 -3.236067976 7.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 20.23606798 -3.236067976 -13.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 9.763932024 3.236067976 7.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 9.763932024 3.236067976 -13.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 9.763932024 -3.236067976 7.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 9.763932024 -3.236067976 -13.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 25.47213596 5.236067976 0.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 25.47213596 5.236067976 -6.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 25.47213596 -5.236067976 0.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 25.47213596 -5.236067976 -6.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 4.527864044 5.236067976 0.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 4.527864044 5.236067976 -6.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 4.527864044 -5.236067976 0.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 8.472135956 4.527864044 -5.236067976 -6.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 25.47213596 5.236067976 0.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 25.47213596 5.236067976 -6.236067976 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 25.47213596 -5.236067976 0.236067976 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 25.47213596 -5.236067976 -6.236067976 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 4.527864044 5.236067976 0.236067976 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 4.527864044 5.236067976 -6.236067976 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 4.527864044 -5.236067976 0.236067976 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -8.472135956 4.527864044 -5.236067976 -6.236067976 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 18.23606798 5.236067976 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 18.23606798 5.236067976 -11.47213596 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 18.23606798 -5.236067976 5.472135956 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 18.23606798 -5.236067976 -11.47213596 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 11.76393202 5.236067976 5.472135956 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 11.76393202 5.236067976 -11.47213596 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 11.76393202 -5.236067976 5.472135956 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ 10.47213596 11.76393202 -5.236067976 -11.47213596 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 18.23606798 5.236067976 5.472135956 ] translate green shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 18.23606798 5.236067976 -11.47213596 ] translate blue shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 18.23606798 -5.236067976 5.472135956 ] translate white shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 18.23606798 -5.236067976 -11.47213596 ] translate yellow shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 11.76393202 5.236067976 5.472135956 ] translate cyan shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 11.76393202 5.236067976 -11.47213596 ] translate magenta shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 11.76393202 -5.236067976 5.472135956 ] translate red shapecolor block4 [.25 .25 .25 .25] scale [ -10.47213596 11.76393202 -5.236067976 -11.47213596 ] translate green shapecolor

by **benb** » Tue Jan 28, 2014 6:26 pm

I've attached an image showing one possible visualization using the code I posted yesterday; it shows the vertices of the 120-cell as if "from above."

by **benb** » Tue Jan 28, 2014 6:29 pm

#2; I've attached an image showing another possible visualization using the code I posted yesterday; it shows the vertices of the 120-cell as if "from within;" only vertical rotation has transpired for the ascent so the original left/right and ana/kata orientations remain intact.

by **quickfur** » Tue Jan 28, 2014 11:50 pm

Yup they sure look like stars to me.

Can't say it really helps me grasp the shape of the 120-cell, though. What about if you insert the 2-faces somehow?

by **benb** » Wed Jan 29, 2014 11:56 am

@quickfur: Seeing the components separately sometimes facilitates recognition of how the structure fits together overall, and sometimes that is only apparent when contrasted with seeing the components in conjunction with one another. To add the 2-faces, I could define each of the edges by the vertices and then define the faces by those edges. I have yet to commit the time to writing/finding a script that will sort the vertices into pairs one unit length apart; calculating the distance between any two is easy, but doing it manually is inefficient. For those who are interested, here is a link to information regarding code generation: http://urticator.net/blocks/v4/language-geom.html

by **quickfur** » Wed Jan 29, 2014 7:06 pm

benb wrote:@quickfur: Seeing the components separately sometimes facilitates recognition of how the structure fits together overall, and sometimes that is only apparent when contrasted with seeing the components in conjunction with one another. To add the 2-faces, I could define each of the edges by the vertices and then define the faces by those edges. I have yet to commit the time to writing/finding a script that will sort the vertices into pairs one unit length apart; calculating the distance between any two is easy, but doing it manually is inefficient. For those who are interested, here is a link to information regarding code generation: http://urticator.net/blocks/v4/language-geom.html

This sounds like just repeating the work of a convex hull algorithm. I already have the full face lattice of the 120-cell (and many other polytopes!) on file, if you're interested. The format is text-based, and a parser should be relatively easy to write. Having the entire face lattice on hand makes things far easier when you need to look things up: instead of needing hack solutions like iterating over all vertex pairs to find those exactly 1 unit apart, you just iterate over the set of edges and read off their vertices.

(I say this because this is exactly what I faced when I was writing my polytope viewer program. Vertices are easy to generate, and any convex hull algorithm will give you the facets, but it wasn't clear to me how to get from there to the edges to be drawn, or the ridges I wanted to highlight. Eventually I decided that the only practical solution for what I needed to do was to just precompute the entire face lattice. After I did that, it was much easier to accomplish things that, arguably, should be easy, but often isn't because the face lattice isn't available.)

by **benb** » Wed Jan 29, 2014 7:34 pm

@quickfur: I'll gladly accept everything you'd care to share; are your text-based face lattices publicly available? (My apologies for drawing this out.)

by **quickfur** » Wed Jan 29, 2014 8:59 pm

benb wrote:@quickfur: I'll gladly accept everything you'd care to share; are your text-based face lattices publicly available? (My apologies for drawing this out.)

Here's the file.

A quick explanation of the format:

lines starting with '#' are comments, and are ignored by the parser.
the identifier following the 'polytope' keyword is just an arbitrary label to identify the polytope; the parser stores it as a string but doesn't attempt to parse it.
the 'dimension' keyword and the 'vertices' block should be obvious. It is important to note, though, that the vertices are assigned sequential numbers starting from 0, and these are the indices used in the face lattice.
the 'lattice' keyword begins the face lattice. The format of entries in this section is: <dimension>, { <vertex0>, <vertex1>, <vertex2>, ... }, where the vertices are referred to by index, as described above. There is no particular order to the entries; face elements of various dimensions may be intermixed.
For (n-1)-dimensional elements, there's an additional, optional, (n+1)-dimensional vector following the vertex set, that defines the hyperplane that the facet lies on (or to be precise, the halfspace that it defines). Strictly speaking this information is redundant, since it can be computed from the vertices, but it's provided in case you don't want to bother with computing n-dimensional cross products. The hyperplane's halfspace is defined by the equation x1*N1 + x2*N2 + ... xn*Nn ≤ N{n+1)}, where (N1,N2,...N{n+1}) is the vector given.

The main reason for the special treatment of halfspaces is because my polytope viewer performs visibility culling by computing the dot product of the hyperplane normal with the camera's location, and skipping the facet if it's facing away from the camera. This information could be useful in an interactive application as well, since visibility culling generally makes 4D projections / whatever visualization method you use more manageable, especially when you're dealing with the sheer immensity of the 120-cell family polytopes with thousands of surface elements.

Edit: I forgot to mention, this is the original 120-cell file I have, so its vertex coordinates are not rescaled to give unit edge length (the edge length here is √5-1), so you have to divide the vertex coordinates by √5-1 (equiv. multiply by φ²/2 where φ is the Golden Ratio) to get unit edge lengths. As long as you don't change the order of vertices while doing so, the rest of the face lattice remains unchanged.

by **Keiji** » Fri Jan 31, 2014 7:35 am

quickfur wrote:
benb wrote:@quickfur: I'll gladly accept everything you'd care to share; are your text-based face lattices publicly available? (My apologies for drawing this out.)

Here's the file.

And because quickfur forgot to answer the actual question, its license is CC-BY-SA 3.0 according to :File/XRAPR5MVE5H5W8YEQ19BWFRAXR where it was uploaded. (Sorry quickfur!

)

by **quickfur** » Fri Jan 31, 2014 4:11 pm

Keiji wrote:
quickfur wrote:
benb wrote:@quickfur: I'll gladly accept everything you'd care to share; are your text-based face lattices publicly available? (My apologies for drawing this out.)

Here's the file.

And because quickfur forgot to answer the actual question, its license is CC-BY-SA 3.0 according to :File/XRAPR5MVE5H5W8YEQ19BWFRAXR where it was uploaded. (Sorry quickfur! )

I'm very forgetful these days. :mrgreen:

by **benb** » Sun Feb 16, 2014 1:20 am

Hopefully you haven't forgotten this! Sorry about the delay. :oops:

http://youtu.be/kS5yoPW_ueA

by **benb** » Sun Feb 16, 2014 8:32 pm

...And here's another!
http://youtu.be/ncHRw37KcR0

by **quickfur** » Mon Feb 17, 2014 3:55 pm

Wow.

That's so pretty! I've to admit I've a hard time understanding what I'm seeing, though. :lol:

There seem to be two vertical discontinuities on either side of the display where the curvature seems to switch directions. I'm not quite sure how to interpret this. Maybe I'll have to re-read the double rainbow display description again... Good job with the animation, though. It's very mesmerizing!

by **benb** » Mon Feb 17, 2014 4:56 pm

I have found interpreting the display to be made easiest by conceiving of it in operational terms, namely regarding it as not only views of what is in front of the user in the context of that user's ana/kata and left/right continua, but also as containing preview or peripheral-type views of what would (or will) appear in front of that user were that user to turn ana or kata or left or right. Most of the changes in the longitudinally-colored video (http://youtu.be/ncHRw37KcR0 or https://archive.org/details/120CellColoredByLongitude) are simply translations of one unit and rotations of ninety degrees from the center of the 120-cell (even when the stage on which the 120-cell is displayed is being rotated).

by **quickfur** » Mon Feb 17, 2014 5:55 pm

benb wrote:I have found interpreting the display to be made easiest by conceiving of it in operational terms, namely regarding it as not only views of what is in front of the user in the context of that user's ana/kata and left/right continua, but also as containing preview or peripheral-type views of what would (or will) appear in front of that user were that user to turn ana or kata or left or right. Most of the changes in the longitudinally-colored video (http://youtu.be/ncHRw37KcR0 or https://archive.org/details/120CellColoredByLongitude) are simply translations of one unit and rotations of ninety degrees from the center of the 120-cell (even when the stage on which the 120-cell is displayed is being rotated).

Ooh I see, so it's actually 6 panels showing the two fronts and their respective laterals?

by **benb** » Mon Feb 17, 2014 6:17 pm

Well said, quickfur!

The "two fronts" are stacked in the center with the ana/kata continuum on top and the left/right continuum on the bottom.
The lateral views are to either side.

by **quickfur** » Mon Feb 17, 2014 6:30 pm

benb wrote:Well said, quickfur!
The "two fronts" are stacked in the center with the ana/kata continuum on top and the left/right continuum on the bottom.
The lateral views are to either side.

OK, but if that's the case, then I'd suggest introducing a separation between the front panels and the left/right panels so that they're not confused with the frontal views.

Also, how is visibility clipping handled in each view? Is it done at all?

by **Keiji** » Mon Feb 17, 2014 6:59 pm

quickfur wrote:OK, but if that's the case, then I'd suggest introducing a separation between the front panels and the left/right panels so that they're not confused with the frontal views.

On the contrary, I like it how it is without separation, as even though the views are discrete, they neatly "merge" at the border, so you can either treat the six panels separately or look at the top/bottom strips as panoramas.

by **benb** » Mon Feb 17, 2014 8:10 pm

I'm sympathetic to both the panorama-as-continuity perspective articulated by Keiji as well as quickfur's suggestion that there ought be some distinction between a frontal view and the lateral views (setting aside questions of clipping for the moment). Perhaps skewing the lateral sections may work as one might view them in terms of perspective. For example, if I am in a box with my back against one wall and if the image of what is in front of me is projected flat against the other wall opposite me, what is to my left and my right may be projected flat to my left and my right, though they would appear to me as if they were skewed such that they were largest closest to me and smallest closest to the projection of what was in front of me. If this skew of two outer squares on either side of a center square were carried out from the existing Double Rainbow Display, the framework for the three objects together might look something like a bow tie for each level (two "bow-ties" in total). If the skew were made more gradually over the entire field of view, it may more closely resemble this ")(" after a ninety-degree rotation.

by **quickfur** » Mon Feb 17, 2014 8:56 pm

benb wrote:I'm sympathetic to both the panorama-as-continuity perspective articulated by Keiji as well as quickfur's suggestion that there ought be some distinction between a frontal view and the lateral views (setting aside questions of clipping for the moment). Perhaps skewing the lateral sections may work as one might view them in terms of perspective. For example, if I am in a box with my back against one wall and if the image of what is in front of me is projected flat against the other wall opposite me, what is to my left and my right may be projected flat to my left and my right, though they would appear to me as if they were skewed such that they were largest closest to me and smallest closest to the projection of what was in front of me. If this skew of two outer squares on either side of a center square were carried out from the existing Double Rainbow Display, the framework for the three objects together might look something like a bow tie for each level (two "bow-ties" in total). If the skew were made more gradually over the entire field of view, it may more closely resemble this ")(" after a ninety-degree rotation.

I like the bowtie idea. It makes it more obvious what's happening without needing to read a verbal explanation. The skew can be relaxed, as you suggest, to be less angular, perhaps even some kind of cylindrical mapping can be used to make the transition between the front and left/right panels smoother.

by **Keiji** » Tue Feb 18, 2014 6:34 am

Maybe just make it optional which display you want?

Hi.gher. Space

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