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Subpolytopes of Cyclic Polytopes

✍ Scribed by Tibor Bisztriczky; Gyula Károlyi

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 85 KB
Volume: 21
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0318

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✦ Synopsis

A remarkable result of Shemer [7] states that the combinatorial structure of a neighbourly 2mpolytope determines the combinatorial structure of each of its subpolytopes. From this, it follows that every subpolytope of a cyclic 2m-polytope is cyclic. In this note, we present a direct proof of this consequence that also yields that certain subpolytopes of a cyclic (2m + 1)-polytope are cyclic.

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