This article is cited in 2 papers

On Simplicial Partitions of Polytopes

A. A. Glazyrin

M. V. Lomonosov Moscow State University

Abstract: We prove some general properties of prismoids, i.e., polytopes all of whose vertices lie in two parallel planes. On the basis of these properties, we obtain a nontrivial lower bound for the number of simplices in a triangulation of the $n$-dimensional cube.

Keywords: prismoid, $(0,1)$-polytope, simplicial partition, triangulation, minimal triangulation, inextensible set.

UDC: 514.154

Received: 15.06.2006
Revised: 23.10.2008

DOI: 10.4213/mzm3889

 English version: Mathematical Notes, 2009, 85:6, 799–806

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