Quickfur's renders

[quickfur]

Wow, Jonathan has moved on to uniform polytera now? Whoa.

What was the last final count of (not necessarily convex) uniform polychora?

[Klitzing]

Wow, Jonathan has moved on to uniform polytera now? Whoa.

What was the last final count of (not necessarily convex) uniform polychora?

Depends on how you'd count. On his site he writes (in the history block)

On my old AOL site (last updated in 2002 - and its now gone), I mentioned that there were 8190 uniform polychora

but there has been a redefinition, canceling out lots of "unusual" things. So his current count is written at the top of his site:

Uniform polychoron count still stands at 1849 plus many fissaries

.

--- rk

[Klitzing]

Hi Quickfur,
no renders this month?
(Thought of having provided enough new possibilities recently, hehe)
--- rk

[quickfur]

I do have a 120-cell family uniform polychoron in the works, but have been very busy with other things, so haven't gotten around to it yet. And yes I've been skimming over your new discoveries. Plus, there are still older discoveries that I wanted to render but haven't had the chance yet. So many new things to render, so little time!

[Klitzing]

As to skimming, I too was skimming through all that Johnson polytope thread. There have been lots of jewels in there. Many of those are now already mentioned in my IncMats website. Even lots of cross-links have been added to your private 4D website. - You probably already noticed.

In the meantime I'm in the run to elaborate my recent topic of partial Stott expansion / contraction a bit further. The actual research at the tetracombs so is harder to do. So I hope to come around quite soon. I even have a comprehensive outline through all those dimensions in reach. So be prepared to what's coming up!

--- rk

[Oschkar]

I do have a 120-cell family uniform polychoron in the works, but have been very busy with other things, so haven't gotten around to it yet. And yes I've been skimming over your new discoveries. Plus, there are still older discoveries that I wanted to render but haven't had the chance yet. So many new things to render, so little time!

It's already June, and there haven't been any new renders for three months. Also, a month is quite a bit of time, especially for rendering computer-generated images of geometric shapes others have already found the coordinates for.

(Also, I’ve found the internet rather boring since quickfur left the HDDB and icarus left DozensOnline.)

[wendy]

(Also, I’ve found the internet rather boring since quickfur left the HDDB and icarus left DozensOnline.)

Another dozener? I am wendy.krieger there. In any case, some of us have real-world lives to wrangle.

[Keiji]

(Also, I’ve found the internet rather boring since quickfur left the HDDB and icarus left DozensOnline.)

quickfur hasn't left, he's just not posting any renders for some reason!

Maybe he ran out of interesting polytopes?

[quickfur]

I have not run out of interesting polytopes -- there are too many interesting CRFs to run out for a long while! I've just been too busy to work on this. But I have been working on the next Polytope of the Month. I started working on it again about a week ago, but I had a server move, so that got delayed a bit. But I should be able to post it sometime this month, hopefully. So sorry for the delays!! (And thanks for posting about it here, it helps motivate me to find some time to work on it. )

Maybe I should work on building up a buffer of POM entries, so that I can keep up with the monthly schedule even when I'm busy.

[Oschkar]

(Also, I’ve found the internet rather boring since quickfur left the HDDB and icarus left DozensOnline.)

Another dozener? I am wendy.krieger there. In any case, some of us have real-world lives to wrangle.

Sexagesimalist, but the concept is the same. I’m aware of your username there.

[quickfur]

Alright, boyz & gals! I finally got my act together and finished up the new Polytope of the Month:



This is the runcitruncated 600-cell, or, more precisely, x5o3x3x. The above image only shows 45 of its 120 x5o3x cells; here are the cells that lie on its equator (3-quator?):



Pretty, huh? There are pentagonal prisms, hexagonal prisms, and truncated tetrahedra here, all in nice symmetric patterns. Well, go read up on it at the runcitruncated 600-cell page! I provided full coordinates for it, too (factored in terms of wendy's apacs and epacs operators to keep it down to size; there are 7200 vertices!).

[Klitzing]

These pics, and esp. those more on your linked site, are well worth the time awaiting!
Great job, quickfur!

--- rk

[quickfur]

These pics, and esp. those more on your linked site, are well worth the time awaiting!
Great job, quickfur!

--- rk

Thanks!

[Oschkar]

Will there been any updates to your website soon?

[quickfur]

Ahh, I've been too busy with other things. But maybe I'll try to get things going again in the new year. Too bad I'll be pretty busy over the end of year holidays too, but we'll see. In the past few days I kinda got back into dabbling with 4D stuff -- considering how to represent polytope cell complexes as a way of interactively finding 4D CRFs by hand ("4D lego", if you will). Found some interesting theorems; but I'll have to post about that another time.

[quickfur]

After multiple requests for more polytopes, I finally got my act together and made a new one:



This is the runcitruncated 120-cell, or, as we say in these parts, x5x3o3x. It has a surface consisting of 120 truncated dodecahedra, 720 decagonal prisms, 1200 triangular prisms, and 600 cuboctahedra. Check out the runcitruncated 120-cell page for the structural projections that account for each cell in this beautiful polychoron. As usual, full Cartesian coordinates are provided.

Some of my favorite structural snapshots:







Since cells of the same type are well-separated, it was possible to assign a single color to each type, which makes for rather nice patterns in the structural projections.

Enjoy!

[Klitzing]

Beautiful renders, as always!
--- rk

[quickfur]

It's that time of the month again!



This is the cantitruncated 120-cell, or x5x3x3o. It can be constructed by the Stott expansion of the decagons of the truncated 120-cell (x5x3o3o). It is bounded by 120 great rhombicosidodecahedra (x5x3x) joined at their decagonal faces, with the gaps filled in by 1200 triangular prisms and 600 truncated tetrahedra.

This is the 2nd last convex uniform polychoron on my website... I'll start on the renders of the last one, x5x3x3x, soon; hopefully it will be done in time for next month, then the coverage of the convex uniform polychora will finally be complete! Then after that, probably some CRFs (the swirldiminished rectified 600-cell, aka spidrox, will be among the candidates) or maybe the 4D Catalans. We will see!

[Keiji]

Awesome, I'd love to see some 4D Catalans.

Alternatively, when you're done with these, maybe some renders of all ten bicupolic rings in the same style as the five we already have would be nice to have on the wiki?

[quickfur]

Awesome, I'd love to see some 4D Catalans.

Me too! I did post a quick render of one of the catalans on this forum a long time ago, but I can't seem to find it now. The search function didn't turn up anything.

Alternatively, when you're done with these, maybe some renders of all ten bicupolic rings in the same style as the five we already have would be nice to have on the wiki?

You do know that one of the bicupolic rings is already up, right?

[Keiji]

Well, I was hoping more for images in the style of the five already on the wiki, so we can complete the pages for the other five.

[quickfur]

Well, I was hoping more for images in the style of the five already on the wiki, so we can complete the pages for the other five.

Ah, you could've just asked, I can make those images for you.

[quickfur]

Well, I was hoping more for images in the style of the five already on the wiki, so we can complete the pages for the other five.

Well, I added the images now, and stub pages for the missing bicupolic rings. I even threw in the digonal gyrobicupolic ring for good measure. And images for J91 and J92.

And btw, the digon orthobicupolic ring isn't degenerate; it would be made of a square connecting two parallel digons, and a perpendicular square on the opposite end connected by a pair of triangular prisms, with tetrahedra and more triangular prisms flanking them. IOW, it is equivalent to the tetrahedral prism.

Similarly, the digon magnabicupolic ring isn't degenerate either; it is a digon opposite a cube (i.e. Stott-expanded digon prism), so it would be equivalent to a square pyramid prism. It has the same pattern of alternating square pyramids / triangular prisms between the digon and the cube, that you see in the bigger bicupolic rings.

So you see, there are really 12 bicupolic rings!

[Keiji]

Oooh! That's really awesome to know.

In that case would you be so kind as to add renders for the same perspectives to the tetrahedral prism and square pyramid prism pages?

And maybe a stereo version of the digonal gyrobicupolic ring image?

[quickfur]

Oooh! That's really awesome to know.

In that case would you be so kind as to add renders for the same perspectives to the tetrahedral prism and square pyramid prism pages?

And maybe a stereo version of the digonal gyrobicupolic ring image?

All done.

[Keiji]

Ooh, thanks for those!

[quickfur]

Sighh... one week in February has already rolled by, and barely any progress on the omnitruncated-120cell page. There are some O(n^2) algorithms in my polytope viewer that's really killing rendering times with the insane number of vertices/edges that the omnitruncated 120-cell has. Maybe the Polytope of the Month for March should be the J92 rhombochoron instead. Or the castellated prism. That should give me enough buffer to get the omni-120cell done at last.

[Keiji]

Hmm, do they really affect it that badly? How long are the renders taking?

[wendy]

The renders look like stereo pairs. (sigh). I really can't see stereo images. But they're beautiful all the same.

[student91]

Sighh... one week in February has already rolled by, and barely any progress on the omnitruncated-120cell page. There are some O(n^2) algorithms in my polytope viewer that's really killing rendering times with the insane number of vertices/edges that the omnitruncated 120-cell has. Maybe the Polytope of the Month for March should be the J92 rhombochoron instead. Or the castellated prism. That should give me enough buffer to get the omni-120cell done at last.

I vote for the J92-rhombochoron!! I would love to undertand it's structure in more depth