Quickfur's renders

[mr_e_man]

On your Uniform Polyhedra page, the "portrait" description is missing the 20-gon prism in the 2nd row.

Haha, I'm not particularly inclined to add it, since there are an infinite number of prisms, and the ones shown are just a few selected ones.

I mean the description doesn't match the picture. The 20-gon prism is in the picture, but it's not in the description.

[mr_e_man]

viewtopic.php?p=19492#p19492

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.

Have you posted that anywhere yet? (Or, do you even remember what you were talking about then?)


viewtopic.php?p=26001#p26001

Also, when coloring a very large polytope, often the surtope subset that needs coloring contains elements that are touching each other, so individual elements have to be assigned different colors. The program currently has no automation for this, so I end up having to solve the graph coloring problem by hand over and over, once per subset of cells to color.

You could add a slight random variation to the colours, so that different cells look different, but still similar enough if they're in the same subset.


viewtopic.php?p=26132#p26132

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).

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?

I also want an answer to this. I didn't find anything on Klitzing's site saying that all 4D convex scaliforms have been found. (Surely not all 4D scaliforms have been found, as the search for 4D non-convex uniforms is on-going.)

[Klitzing]

viewtopic.php?p=26132#p26132

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).

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?

I also want an answer to this. I didn't find anything on Klitzing's site saying that all 4D convex scaliforms have been found. (Surely not all 4D scaliforms have been found, as the search for 4D non-convex uniforms is on-going.)

No proof is known to me either. Wrt. the convex polychora it is. For the non-convex ones the search obviously is on-going.
--- rk

[quickfur]

I've been meaning to do this, but haven't gotten to around to it until now: my website has moved. The website itself hasn't changed, but I've switched to a different domain name: https://www.qfbox.info/4d/. The old domain name will remain active until next year, then it will be permanently deleted. Please update your bookmarks! All URL paths remain the same, except for the hostname. So it shouldn't be too hard to update any existing bookmarks/links you have. (In theory, anyway. )

[username5243]

I've been meaning to do this, but haven't gotten to around to it until now: my website has moved. The website itself hasn't changed, but I've switched to a different domain name: https://www.qfbox.info/4d/. The old domain name will remain active until next year, then it will be permanently deleted. Please update your bookmarks! All URL paths remain the same, except for the hostname. So it shouldn't be too hard to update any existing bookmarks/links you have. (In theory, anyway. )

Someone on the Polytope Wiki already seems to have changed it a while ago. I let Klitzing know elsewhere and all his links should be fixed whenever he next updates. I let Bowers know too so he hopefully will when he updates in the near future (we've been doing a lot of non-convex searching lately, he's got a lot of things to update). I can't think of any other links that need updated...

[quickfur]

It's been a while, but I finally got around to updating my website again. I'm starting the Catalan project -- to cover all the Catalans: 3D first, then the dual prisms and antiprisms, then the 4D catalans. Starting out small, with the relatively small triakis tetrahedron:



I actually already have the next 3 Catalans lined up, but will post only one per month to give myself enough buffer to keep things going. Hopefully I'll be able to keep going until I finish the 4D catalans!