Quickfur's renders

[quickfur]

This month's Polytope of the Month is the runcinated snub 24-cell:



Nothing new here, but this is the last of the known scaliform polychora on my website, so it seems like a natural thing to follow after spidrox. Some of my favorite renders:



(showing the pyritohedral symmetry of the cupolae)



(showing the cells that lie on the projection envelope).

[username5243]

Nothing new here, but this is the last of the known scaliform polychora on my website, so it seems like a natural thing to follow after spidrox.

Actually, there's one more convex scaliform polytope you haven't posted yet - tutcup (truncated tetrahedral cupolipirsm), which has 2 truncated tetrahedra, 6 tetrahedra, and 8 triangular cupolae. It is a segmentotope whose bases are two oppositely oriented truncated tetrahedra.

[quickfur]

Nothing new here, but this is the last of the known scaliform polychora on my website, so it seems like a natural thing to follow after spidrox.

Actually, there's one more convex scaliform polytope you haven't posted yet - tutcup (truncated tetrahedral cupolipirsm), which has 2 truncated tetrahedra, 6 tetrahedra, and 8 triangular cupolae. It is a segmentotope whose bases are two oppositely oriented truncated tetrahedra.

Ooh! Thanks for the tip! I'll be sure to post that next month!

Are all of the convex scaliforms already known? Or are these only the currently-known ones?

[Mercurial, the Spectre]

Nothing new here, but this is the last of the known scaliform polychora on my website, so it seems like a natural thing to follow after spidrox.

Actually, there's one more convex scaliform polytope you haven't posted yet - tutcup (truncated tetrahedral cupolipirsm), which has 2 truncated tetrahedra, 6 tetrahedra, and 8 triangular cupolae. It is a segmentotope whose bases are two oppositely oriented truncated tetrahedra.

Ooh! Thanks for the tip! I'll be sure to post that next month!

Are all of the convex scaliforms already known? Or are these only the currently-known ones?

Definitely yes in 4D. They are related to a specific convex uniform polychoron (ex. tutcup-sircope, bidex-ex, and prissi-prico).

[quickfur]

Not sure I understand. Are you saying we know all of them, or these are the only ones we know of? If the former, do we have proof that there are no others?

[quickfur]

Anyways, in the meantime, I've been adding the Johnson solids to my website, and today came to J32, which is an EKF of the icosahedron. So I made an animation of it:



I know you guys have been asking for this for a long time... well I finally got round to it.

[quickfur]

Hmm, apparently I forgot to post this month's POM here:



Y'all probably can already guess what this is, so I leave it as an exercise for the reader.

[quickfur]

Ahh, how many months have gone by and I haven't posted the latest POMs. But here they are (click on image to visit the respective page):

July:

August:

September:

October:

[quickfur]

I seem to keep forgetting to update this thread. Here are the latest renders:

November:


December:


January 2019:


I know, I know, sorry, been pretty busy lately so haven't been able to do much rendering work on the non-trivial CRFs, so I fell back to just picking interesting members among the segmentochora for rendering. Well, actually, not even interesting members necessarily, but just simple ones that I happen to have the model files handy for.

And my buffer has been exhausted since 2-3 months ago (that's why the last few POMs have been late), so I'm gonna hafta build up my Polytope of the Month buffer again. I've been wanting to render some of the more interesting CRFs that I still haven't gotten around to, but I haven't dared so far because of the pressure of needing to come up with next month's POM entry. (And I'm afraid to take a month off, because the last time I did that, that month lasted almost 4 years. ) So I gotta build up another buffer of relatively simple CRFs for the next couple o' months so that I can work on the more interesting ones.

[Dekeract]

Can you do rotating in hyperspace views for all your POMs? I just love the gif files of polychora. Also, can your program render 5+ dimensional figures? If so can you render a Dekeract (a ten dimensional analog of a cube or a rectangular prism) for me??

Thanks

[quickfur]

Can you do rotating in hyperspace views for all your POMs? I just love the gif files of polychora. Also, can your program render 5+ dimensional figures? If so can you render a Dekeract (a ten dimensional analog of a cube or a rectangular prism) for me??

Thanks

In theory I do have a script that can do polychora animations pretty easily. The catch is that producing good animations require a bit more work, sometimes a lot more. The main tricky part is to come up with a good coloring scheme that will still look OK under rotations. Most of the static renders have little tweaks here and there to make the result look better. But in an animation I cannot just tweak individual frames, since it will look out-of-place like flickering; I have to come up with a color scheme that looks good from every rendered angle, which is a lot harder.

But I'll definitely keep this in mind for the future.

As for figures that are 5D or above, my program can load them and manipulate them, but the rendering code only works for 3D or 4D. So sorry, 10D will have to wait. But in case you were wondering, projections of higher-dimensional cubes generally look like zonohedra / zonotopes of some kind.

[Dekeract]

Can you maybe do some complex segmentochora for a few POMs. I like how segmentochora look when they are based on relatively complicated polyhedra

[quickfur]

I do plan do to a lot of interesting CRFs, it's just that I've limited time to work on them. There's a lot of CRFs that I'd like to render, the goal eventually is to render all of the known ones. That includes a lot of the interesting uniform polychora diminishings, and EKF polychora, and a bunch of others. The segmentochora are basically "filler" while I work on the others.

[quickfur]

Mighty quiet here lately.

Anyway, February's POM is a nice little polychoron that sports gyrobifastigium (J26) cells, the augmented cantitruncated 5-cell:



I know, I know, nothing big and complex. But I thought the gyrobifastigium cells are interesting enough in their own right to deserve a POM entry. I was going to do an animation, but ran out of time to do it. So many CRFs to render, so little time!

[Dekeract]

POM update???

[Klitzing]

Hehe, he did so, cf. http://eusebeia.dyndns.org/4d/index,
he just forgot to mention here.

--- rk

[quickfur]

Yeah, sorry. Been away from here for a while now. Here are the entries for the past 3 months:

March:


April:


May:

[quickfur]

This week I posted the last of the Johnson solids on my website. To commemorate this landmark event, I created a family portrait of the Johnson solids:



(High resolution version available from the Johnson solids page. Enjoy!!!)

This image actually shows 97 rather than 92 solids, because the 5 chiral Johnson solids are paired with their respective mirror-images.

This particular layout has some very neat coincidences:

I didn't want to relegate the crown jewels to the far back of the image, since they are among the most interesting and unique of the Johnson solids; so I decided to put them in the front. There are 9 of them, and following them are the 6 basic prismatic solids (the pyramids and cupolae). So this suggests the breakdown 4+5 followed by 6, thus leading to the truncated triangular arrangement you see above. Since 4 + 5 + 6 + ... is just the difference of two triangular numbers, in particular T(n) - T(3), and it so happens that T(14) - T(3) = 99, that means the first 10 rows can follow the formation of T(13) - T(3) = 85, then the last row can repeat the 3rd last row of 12 elements, thus maintaining the hexagonal packing and forming a truncated triangular boundary.

And it just so happens that since the crown jewels were moved to the front, the last row of 12 solids exactly coincided with the modifications of the rhombicosidodecahedron -- they all fit in exactly one row.

This triangular layout is also a nice layout for the perspective projection of the camera, so that everything fits nicely in the 3D scene.

Another coincidence is that J26, the gyrobifastigium, appears more-or-less in the center of the layout, being the unique digonal cupola derivative counted among the Johnson solids.

Originally, I had only 92 solids in the layout, but that led to an ugly last row. Adding in the 5 enantiomers of J44-J48 pushed the total up to 97, exactly T(3)+2 short of T(15)=105, thus allowing for the present nice, symmetrical layout.

P.S., I've derived / found from published papers exact algebraic coordinates for all of the Johnson solids, from which arbitrary-precision coordinate values may be obtained. They are posted on the respective Johnson solid's page on my website, so if you ever have a research project that required exact coordinates for the Johnson solids, now you know where to find them.

[Dekeract]

POM update????? I keep checking this forum and the euesbia site but still none! Hurry up, I thought u had a buffer of polytopes.

[quickfur]

My buffer ran out. Well, actually there is still one polytope left, but it's only half-finished, so not ready for posting yet.

[Dekeract]

POM update??????????

[student91]

Relax, quickfur puts quite a lot of effort into making these renderings. Just be happy at the times there is a new rendering

[Mecejide]

Why is this thread in Other Polytopes instead of CRF Polytopes?

[Klitzing]

This is due to the fact that Quickfur joined the board way before the CRF thread was set up …
In fact that thread once was designed to cut down the now closed thread on higher dimensional Johnson solids.
And even there Quickfur already had posted his very good renders.

--- rk

[Dekeract]

POM update???????!??

[Ariel Schnee]

Today I made the Coolest Animation Ever:

I have no idea what this is, but it's totally AWESOME!^_^

I was just looking around on Google (Images), and I saw this. Clicked on the link, and wound up here. I just had to say how great this is, and how amazing you are to have made it.^_^

Do you have a bigger version somewhere?

Now I'm convinced that the next chapter on rotation in my 4D visualization document will take the 120-cell (and its family) as the primary object of study. :)

I couldn't find this .gif anywhere on that page. But then again, I have no idea what any of this is. So I probably wouldn't know where to look.

Anyway, great .gif here. It's soooooo cool! It looks like something on Doctor Who!^_^

---

Signature

[student91]

I couldn't find this .gif anywhere on that page. But then again, I have no idea what any of this is. So I probably wouldn't know where to look.

You can find it on this page: http://eusebeia.dyndns.org/4d/runci120cell
If you want to know what all this is, you can take a look at for example this page: http://eusebeia.dyndns.org/4d/uniform

I really think quickfurs site explains it very well.

[Dekeract]

When will u do a POM update on Eusebia site?

[quickfur]

Sorry, been very busy with other projects. No timeline set at the moment.

[Mercurial, the Spectre]

Might be interesting if you could explore these polytopes:
1. swirlprisms (isogonal, can have prime numbers of vertices)
2. non-uniform alternates (e.g. alternated omnitruncated 5-cell and alternated truncated octahedral prism)