Isogonal swirl polychora

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

Isogonal swirl polychora

Postby Mercurial, the Spectre » Sat Sep 21, 2019 8:53 pm

I think Bowers has discovered many dice that are very interesting to look at, but unfortunately I don't have access to Stella4D, polyview, or any other 4D rendering software to check with. Unfortunately from what I can find, Stella4D is not free and polyview is not available in Windows.

I have heard of examples such as the 72 square antiprism dice and the 250 sided corkscrew dice. Sounds like their duals are isogonal as well, although I have no idea of the 4D coordinates or any images related to these shapes. But fortunately he mentioned the 16-celled tetrahedral swirl dice which has D3 symmetric cells.

So far I only use GeoGebra to make 3D orthogonal projections of 4D objects. It takes a lot of time to put the vertices and edges. It took me a week to make an F4-centered projection of the omnisnub 24-cell (basically two different 24-gonal projections). For the coordinate transforms I use Wolfram Alpha.

Would you help me join the hunt for these elusive isogonal polychora?

PS. Came back because I forgot to visit this site, just going back to regular isogonal polychoron hunting. I know many of you have searched for CRFs, but why not take a look into the world of isogonal nonuniform polychora? Like the alternated biomnitruncatodecachoron formed as an alternated biomnitruncatodecahoron (convex hull of two omnitruncated 5-cells with two kinds of truncated octahedra) I added in wikipedia.
SárHwās Hnáras táygʲasi Hr̥táy kʲa waĉatás samHatás kʲa ĵn̥Hyántay. Táy kʲitˢtáH mánasaH kʲa dádHn̥tay Hántaray práti bʰraHtrásya pn̥tHáH kriHánt.

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Mercurial, the Spectre
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Joined: Mon Jun 19, 2017 9:50 am

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