Explore: Convex Polytopes

convex polytopes are often simply called "polytopes". Grünbaum points out that this is solely to avoid the endless repetition of the word "convex",

following table lists some properties of the six convex regular 4-polytopes. The symmetry groups of these 4-polytopes are all Coxeter groups and given in the notation

Convex Polytopes is a graduate-level mathematics textbook about convex polytopes, higher-dimensional generalizations of three-dimensional convex polyhedra

cell, consists of a polyhedron. A polytope may be convex. The convex polytopes are the simplest kind of polytopes, and form the basis for several different

related to the infinite 2D square tiling. Convex 4-polytopes can be cut and unfolded as nets in 3-space. A 4-polytope is a closed four-dimensional figure.

A.; Fukuda, K. (2000), "Exact Volume Computation for Polytopes: A Practical Study", Polytopes — Combinatorics and Computation, pp. 131–154, CiteSeerX 10

treatment of the polytopes regularly derived from the regular polytopes, followed Boole-Stott's notations, enumerating the convex uniform polytopes by symmetry

the convex hulls of indicator vectors of solutions to a combinatorial problem. If the facets of these polytopes can be found, describing the polytopes as

regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. Only counting polytopes of

name hexadecachoron or 16-cell. It is one of the six convex regular 4-polytopes. These 4-polytopes were first described by the Swiss mathematician Ludwig