On Gale and braxial polytopes
摘要
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.
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引用
@article{arxiv.math/0610940,
title = {On Gale and braxial polytopes},
author = {Margaret M. Bayer and Tibor Bisztriczky},
journal= {arXiv preprint arXiv:math/0610940},
year = {2007}
}
备注
15 pages