Abstract Polytope

An abstract polytope is a partially ordered set, whose elements we call faces, satisfying the 4 axioms:

  1. It has a least face and a greatest face.
  2. All flags contain the same number of faces.
  3. It is strongly connected.
  4. Every 1-section is a line segment.

An n-polytope is a polytope of rank n.

Read more about Abstract PolytopeExamples of Higher Rank, Duality, Abstract Regular Polytopes, Realizations, The Amalgamation Problem and Universal Polytopes, Exchange Maps, Incidence Matrices, History

Other articles related to "abstract polytope, abstract polytopes, polytopes, polytope, abstract":

Abstract Polytope - History
... An early example of abstract polytopes was the discovery by Coxeter and Petrie of the three infinite structures {4, 6}, {6, 4} and {6, 6}, which they called regular ... geometric community to consider generalizations of the concept of regular polytopes that he called polystromata ... Grünbaum also discovered the 11-cell, a self-dual 4-polytope whose facets are not icosahedra, but are "hemi-icosahedra" — that is, they are the shape one gets if one considers opposite faces ...
Regular Polytope - History of Discovery - Abstract Polytopes - Vertex Figure of Abstract Polytopes
... is also defined differently for an abstract polytope ... The vertex figure of a given abstract n-polytope at a given vertex V is the set of all abstract faces which contain V, including V itself ... More formally, it is the abstract section Fn / V = {F

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