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.

All human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.
Mercurial, the Spectre
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