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Polytopes with Centrally Symmetric Faces

Published online by Cambridge University Press:  20 November 2018

G. C. Shephard
G. C. Shephard*
Affiliation:
University of East Anglia, England
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If a convex polytope P is centrally symmetric, and has the property that all its faces (of every dimension) are centrally symmetric, then P is called a zonotope. Zonotopes have many interesting properties which have been investigated by Coxeter and other authors (see (4, §2.8 and §13.8) and (5) which contains a useful bibliography). In particular, it is known (5, §3) that a zonotope is completely characterized by the fact that all its two-dimensional faces are centrally symmetric.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1206 - 1213
Copyright
Copyright © Canadian Mathematical Society 1967

References

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