mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying...

manifolds including spherical polyhedra, and set-theoretic abstract polytopes. Polytopes of more than three dimensions were first discovered by Ludwig...

Note, however, that this definition does not work for abstract polytopes. A regular polytope can be represented by a Schläfli symbol of the form {a,...

chains of its faces, and an abstract polytope of rank n is called an abstract n-polytope.: 22–25  For abstract polytopes of rank 2, this means that: A) the...

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

In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular...

24-cell, 120-cell, 600-cell Abstract regular polytope 11-cell, 57-cell Schläfli–Hess 4-polytope (Regular star 4-polytope) Icosahedral 120-cell, Small...

face, an edge of the face, a vertex of the edge, and the null polytope. An abstract polytope is said to be regular if its combinatorial symmetries are transitive...

and is sometimes said to correspond to the null polytope. An abstract polyhedron is an abstract polytope having the following ranking: rank 3: The maximal...

geometry, an apeirotope or infinite polytope is a generalized polytope which has infinitely many facets. An abstract n-polytope is a partially ordered set P...