Uniform Polytopes 2-4 dimensions summary

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

Uniform Polytopes 2-4 dimensions summary

Postby ytrepus » Thu Feb 06, 2014 11:31 pm

Hello everyone,

I posted this as a reply on another thread, but I wanted to share a spreadsheet I put together summarizing the uniform polytopes from 2-4 dimensions. It's still a work in progress and I would love to add more about Coxeter diagrams and dimensions higher than 4.

Would love to hear your thoughts and ideas, and please let me know if you spot any errors (there very well may be plenty).

Note that on the duoprism and appip calc pages you can enter values for p and q to calculate data for those polychora.

https://drive.google.com/file/d/0B4ZHyL ... sp=sharing
(Note you can see a preview before downloading, but Google doesn't do a great job of displaying the sheet -- so if you trust it please download to open in Excel -- there are no macros.)

Thanks again,
Rob
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Re: Uniform Polytopes 2-4 dimensions summary

Postby ytrepus » Thu Feb 06, 2014 11:33 pm

Oops, I should clarify that this only covers CONVEX polytopes.

Thanks a lot,
Rob
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Re: Uniform Polytopes 2-4 dimensions summary

Postby wendy » Thu Feb 20, 2014 8:11 am

http://os2fan2.com/uniform.html

Here i have arranged the uniforms so that all of the prisms are handled as well. The trick is to map 'dodecahedron' and 'dodecahedral prism' onto the same number. The discussion then runs through the dimensions, with something like (at the beginning of 4D), 1, the tesseract, "2..20", line-prisms of the 3d uniforms. 21, the duoprisms BB, and then 22-67 new uniforms. (the teseract is repeated between 23 and 24, to fill its spot in the platonics).
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