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Simplicial faces and sections of a convex polytope

Published online by Cambridge University Press:  26 February 2010

Daniel A. Marcus
Daniel A. Marcus
Affiliation:
California State Polytechnic University, Pomona, California, U.S.A.
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Abstract

For a convex polytope P, let s(P) and σ(P) denote, respectively, the largest t such that P has a t-dimensional face (section) which is a simplex. Using Gale diagrams, lower bounds are obtained for these numbers and formulae are developed for the behaviour of s and σ over Cartesian and other products.

Type
Research Article
Information
Mathematika , Volume 29 , Issue 1 , June 1982 , pp. 119 - 127
Copyright
Copyright © University College London 1982

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References

1.Davis, C.. Theory of positive linear dependence. Amer. J. Math., 76 (1954), 733746.CrossRefGoogle Scholar
2.Gale, D.. Neighboring vertices on a convex polyhedron. In Linear Inequalities and Related Systems, ed. Kuhn, and Tucker, (Princeton, 1956), 255263.Google Scholar
3.Griinbaum, B.. Convex Polytopes (Interscience, New York, 1967).Google Scholar
4.Griinbaum, B.. Polytopes, graphs, and complexes. Bull. Amer. Math. Soc., 76 (1970), 1131–1201.CrossRefGoogle Scholar
5.Marcus, D.. Gale diagrams of convex polytopes and positive spanning sets of vectors. To appear.Google Scholar
6.McMullen, P.. Constructions for projectively unique polytopes. Discrete Math., 14 (1976), 347–358.CrossRefGoogle Scholar
7.McMullen, P.. Transforms, diagrams and representations. In Contributions to Geometry, ed. Tolke, J. and Wills, J. M. (Birkhauser, Basel, 1979), 92–130.CrossRefGoogle Scholar
8.Perles, M. A. and Shephard, G. C.. Facets and non-facets of convex polytopes. Acta Math., 119 (1967), 113–145.CrossRefGoogle Scholar