mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying...
34 KB (4,530 words) - 22:20, 16 September 2023
manifolds including spherical polyhedra, and set-theoretic abstract polytopes. Polytopes of more than three dimensions were first discovered by Ludwig...
26 KB (3,117 words) - 08:04, 5 March 2024
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,...
41 KB (5,265 words) - 03:57, 8 February 2024
Apeirogon (redirect from Abstract apeirogon)
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...
10 KB (1,037 words) - 03:13, 2 March 2024
regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. Only counting polytopes of...
97 KB (5,294 words) - 16:02, 26 March 2024
In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular...
27 KB (1,648 words) - 01:38, 10 April 2024
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...
47 KB (3,585 words) - 04:52, 23 May 2024
Polyhedron (redirect from 3-polytope)
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...
86 KB (9,737 words) - 18:21, 23 March 2024
Regular polyhedron (redirect from Regular 3-polytope)
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...
32 KB (3,118 words) - 14:26, 10 April 2024
Apeirotope (redirect from Abstract apeirotope)
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...
4 KB (435 words) - 17:56, 2 May 2024