# Polytopes

### Some articles on polytope, polytopes:

Chiral Polytope
... In mathematics, there are two competing definitions for a chiral polytope ... One is that it is a polytope that is chiral (or "enantiomorphic"), meaning that it does not have mirror symmetry ... By this definition, a polytope that lacks any symmetry at all would be an example of a chiral polytope ...
Polyhedral Combinatorics
... problems of counting and describing the faces of convex polyhedra and higher dimensional convex polytopes ... Mathematicians in this area study the combinatorics of polytopes for instance, they seek inequalities that describe the relations between the numbers of ... research into precise descriptions of the faces of certain specific polytopes (especially 0-1 polytopes, whose vertices are subsets of a hypercube) arising ...
Geometric Combinatorics
... include metric geometry of polyhedra, such as the Cauchy theorem on rigidity of convex polytopes ... The study of regular polytopes, Archimedean solids, and kissing numbers is also a part of geometric combinatorics ... Special polytopes are also considered, such as the permutohedron, associahedron and Birkhoff polytope ...
Two-dimensional Space - Two-dimensional Geometry - Polytopes - Non-convex
... There exist infinitely many non-convex regular polytopes in two dimensions, whose Schläfli symbols consist of rational numbers {n/m} ...
Chiral Polytope - Polytopes Without Mirror Symmetry
... Many polytopes lack mirror symmetry, and in that sense form chiral polytopes ... It is possible for polytopes to have a high degree of symmetry, but yet to lack mirror symmetry an example is the snub cube, which is vertex-transitive and ...