4-polytope - Wikipedia
In geometry, a 4-polytope (sometimes also called a polychoron, [1] polycell, or polyhedroid) is a four-dimensional polytope. [2][3] It is a connected and closed figure, composed of lower …
Regular 4-polytope - Wikipedia
In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra in three dimensions and the …
Uniform 4-polytope - Wikipedia
In geometry, a uniform 4-polytope (or uniform polychoron) [1] is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons. …
Polytope -- from Wolfram MathWorld
6 天之前 · Coxeter (1973, p. 118) defines polytope as the general term of the sequence " point, line segment, polygon, polyhedron, ...," or more specifically as a finite region of -dimensional …
Polychoron - Simple English Wikipedia, the free encyclopedia
In geometry, a polychoron (plural: polychora) is a figure in four dimensions. The word comes from Greek poly, which means many and choros which means room, or space. Sometimes the …
Regular Polychoron -- from Wolfram MathWorld
3 天之前 · The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by consideration of the …
Regular polychoron - Polytope Wiki
A regular polychoron is a polychoron whose flags are identical under its symmetry group. In 4D Euclidean space, there are 16 finite regular polychora and 1 honeycomb that are not skew, …
Polychoron -- from Wolfram MathWorld
3 天之前 · Weisstein, Eric W. "Polychoron." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Polychoron.html. A polytope in four dimensions. Polychora are …
Uniform Polychora and Other Four Dimensional Shapes
A polychoron is uniform if its vertices are congruent and all of it's cells are uniform polyhedra. A polychoron is a four dimensional polytope, where a polytope must be monal, dyadic, and …
soft question - Simplest Proof of the Six Regular 4-Polytopes ...
2017年2月21日 · The idea is to consider the dihedral angle between adjacent faces for each of the five Platonic solids – a polychoron will consist of instances of one such solid. For the …