Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T18:51:39.318Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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