Maniplex

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{3,2}π is a regular maniplex but not an abstract polytope.

A maniplex is a combinatorial model of polytopes.

Maniplexes can be thought of as complexes with a version of dyadicity.

Definition[edit | edit source]

Edge-colored graph[edit | edit source]

Permutation sequence[edit | edit source]

An n -maniplex is tuple , where Ω  is a set, and A  is a sequence of n  permutations on Ω , :

  1. is a complex.
  2. For any element, a , of the complex, the image of a  under is also an element of the complex.
  3. Every facet of the complex is a maniplex.

The second requirement can be seen as a form of dyadicity, however because maniplexes retain more information than just incidence the same facet of a maniplex can meet itself at a ridge.

Related concepts[edit | edit source]

Abstract polytopes[edit | edit source]

Maps[edit | edit source]

Bibliography[edit | edit source]

  • Garza-Vargas, Jorge; Hubard, Isabel (7 July 2018). "Polytopality of Maniplexes" (PDF). arXiv:1604.01164.
  • Wilson, Steve (2012). "Maniplexes: Part 1: Maps, Polytopes, Symmetry and Operators". Symmetry. doi:10.3390/sym4020265.