Quickfur's renders

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

Re: Quickfur's renders

Postby mr_e_man » Fri Dec 03, 2021 3:24 am

quickfur wrote:
mr_e_man wrote: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.
ΓΔΘΛΞΠΣΦΨΩ αβγδεζηθϑικλμνξοπρϱσςτυϕφχψωϖ °±∓½⅓⅔¼¾×÷†‡• ⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎
ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
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Re: Quickfur's renders

Postby mr_e_man » Thu Jul 28, 2022 6:24 pm

viewtopic.php?p=19492#p19492
quickfur wrote: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
quickfur wrote: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. :D

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
Mercurial, the Spectre wrote:
quickfur wrote:
username5243 wrote:
quickfur wrote: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! :lol: :nod:

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 wrote: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.)
ΓΔΘΛΞΠΣΦΨΩ αβγδεζηθϑικλμνξοπρϱσςτυϕφχψωϖ °±∓½⅓⅔¼¾×÷†‡• ⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎
ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
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Re: Quickfur's renders

Postby Klitzing » Fri Jul 29, 2022 8:59 pm

mr_e_man wrote:viewtopic.php?p=26132#p26132
Mercurial, the Spectre wrote:
quickfur wrote:
username5243 wrote:
quickfur wrote: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! :lol: :nod:

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 wrote: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
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Re: Quickfur's renders

Postby quickfur » Fri Jul 29, 2022 9:29 pm

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! :D 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. :P)
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Re: Quickfur's renders

Postby username5243 » Sat Jul 30, 2022 2:35 am

quickfur wrote: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! :D 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. :P)


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...
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