Uniform polytopes

[mecejide]

About the author

Someone weirdly fixated on uniform polytopes and related math.

Quick Summary

Explains what a uniform polytope is and how to construct many of them.

Target medium

Preferably a Youtube video

More details

This is aimed at someone who has already seen jan Misali’s regular polyhedra video and who knows how higher spatial dimensions work.

Topics discussed: Uniform polytopes Coxeter groups Coxeter-Dynkin diagrams Wythoffian construction Compounds Blending

Contact details

On Discord (Mecejide#2099)

Additional context

The Polytope Wiki is (for the most part) a great source of polytope-related info.

[alan2here]

related:

Space with (constant) negative curvature (hyperbolic space), where even in just 2D and 3D a lot works that would otherwise need Hilbert space. It gigantically expands the pallet of possible uniform polytopes.

Going beyond even fixing a specific type of space with "Abstract Polytopes" (see "Hass" diagrams)

If it's possible to make fair dice out of polytopes, the answer is yes if the same shaped faces (facet with 2nd to maximum rank?) are used for the dices numbers.

Combinatorics and highly composite numbers.

[mecejide]

related:

Space with (constant) negative curvature (hyperbolic space), where even in just 2D and 3D a lot works that would otherwise need Hilbert space. It gigantically expands the pallet of possible uniform polytopes.

Going beyond even fixing a specific type of space with "Abstract Polytopes" (see "Hass" diagrams)

If it's possible to make fair dice out of polytopes, the answer is yes if the same shaped faces (facet with 2nd to maximum rank?) are used for the dices numbers.

Combinatorics and highly composite numbers.

What was the point of saying that?

[alan2here]

They're other highly related aspects to the topic that could be covered. I agree that polytopes are really amazing objects.

[alan2here]

I'm looking forward to you covering Coxeter diagrams and groups in the video.