On Gale and braxial polytopes

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Cyclic polytopes are characterized as simplicial polytopes satisfying Gale's evenness condition (a combinatorial condition on facets relative to a fixed ordering of the vertices). Periodically-cyclic polytopes are polytopes for which certain subpolytopes are cyclic. Bisztriczky discovered a class of periodically-cyclic polytopes that also satisfy Gale's evenness condition. The faces of these polytopes are braxtopes, a certain class of nonsimplicial polytopes studied by the authors. In this paper we prove that the periodically-cyclic Gale polytopes of Bisztriczky are exactly the polytopes that satisfy Gale's evenness condition and are braxial (all faces are braxtopes). The existence of other periodically-cyclic Gale polytopes is open.
15 pages

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Combinatorics, 52B12

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http://salesiana.dossiersoluciones.com/handle/123456789/118186

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610940
 http://arxiv.org/abs/math/0610940

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arXiv