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Diagrams for centrally symmetric polytopes

Published online by Cambridge University Press:  26 February 2010

P. McMullen  and
G. C. Shephard
P. McMullen
Affiliation:
School of Mathematics and Physics, University of East Anglia.
G. C. Shephard
Affiliation:
School of Mathematics and Physics, University of East Anglia.
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Extract

In a paper [1] published in 1956, David Gale introduced the idea of representing a convex polytope by a diagram (now called a Gale diagram). Later work by Gale, T. S. Motzkin, and more recently by M. A. Perles and B. Grünbaum, has shown the importance of this idea. Using it, a large number of results which were formerly inaccessible have been proved. For an account of Gale diagrams and their applications, the reader is referred to Grünbaum's recent book [2; §5.4 and §6.3] and we shall largely follow the notations used there.

Type
Research Article
Information
Mathematika , Volume 15 , Issue 2 , December 1968 , pp. 123 - 138
Copyright
Copyright © University College London 1968

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References

1.Gale, D., “Neighboring vertices on a convex polyhedron”, Linear inequalities and related systems, edited by Kuhn, H. W. and Tucker, A. W. (Princeton, 1956), 255–263.Google Scholar
2.Grünbaum, B., Convex polytopes (John Wiley and Sons: London–New York–Sydney, 1967).Google Scholar