Abstract.
Let P denote a simplicial convex 2m-polytope with n vertices. Then the following are equivalent: (i) P is cyclic; (ii) P satisfies Gale’s Evenness Condition; (iii) Every subpolytope of P is cyclic; (iv) P has at least 2m+2 cyclic subpolytopes with n−1 vertices if n ≥ 2m+5; (v) P is neighbourly and has n universal edges.
We present an additional characterization based upon an easily described point arrangement property.
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Bisztriczky, T. Characterizations of cyclic polytopes. J. geom. 84, 30–36 (2006). https://doi.org/10.1007/s00022-005-0020-2
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DOI: https://doi.org/10.1007/s00022-005-0020-2