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Linearly Stable Polytopes

Published online by Cambridge University Press:  20 November 2018

P. McMullen
P. McMullen*
Affiliation:
University of East Anglia, Norwich, U.K.; Michigan State University, East Lansing, Michigan
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Our aim in this paper is to describe a new class of convex polytopes, which will be called linearly stable. These have properties analogous to those of projectively stable polytopes (called projectively unique by Grunbaum (1, exercise 4.8.30)), which were first investigated early in 1966 by Grunbaum and Pedes. Although many particular examples of projectively stable polytopes have been found, at present no general criteria for projective stability are known.

The main result of this paper is a theorem which enables us to classify linearly stable polytopes completely.

I wish to thank Professor G. C. Shephard for his many helpful suggestions for improvements to this paper. During the period of this research I held a research studentship, for which I would like to thank the Science Research Council.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 1427 - 1431
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Griinbaum, B., Convex polytopes (Wiley, New York, 1967).Google Scholar