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A Counterexample to a Classification Theorem of Linearly Stable Polytopes

Published online by Cambridge University Press:  20 November 2018

David Assaf
David Assaf*
Affiliation:
Hebrew University, Jerusalem, Israel
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We give an example of a centrally symmetric 5-polytope which is linearly stable though its vertices do not form a subset of the vertices of a 5-cube. This example contradicts the “only if” part of the classification theorem on linearly stable poly topes stated by P. McMullen [2]. Moreover the example gives a 5-polytope, the vertices of which form a subset of a 5-cube while its dual does not possess the same property.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 92 - 93
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Grunbaum, B., Convex polytopes (Wiley, New York, 1967).Google Scholar
2. McMullen, P., Linearly stable polytopes, Can. J. Math., 21 (1969), 1427–1431.Google Scholar