# Maniplex

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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]

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### 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 , :

- is a complex.
- For any element, a , of the complex, the image of a under is also an element of the complex.
- 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]

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### Maps[edit | edit source]

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## 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.

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