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 Polytope:  Examples of Higher Rank, Duality, Abstract Regular Polytopes, Realizations, The Amalgamation Problem and Universal Polytopes, Exchange Maps, Incidence Matrices, History

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    —Georg Wilhelm Friedrich Hegel (1770–1831)