leios
Uniform polytopes
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.
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.
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?
They're other highly related aspects to the topic that could be covered. I agree that polytopes are really amazing objects.
I'm looking forward to you covering Coxeter diagrams and groups in the video.