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Combinatorial Properties of Associated Zonotopes

Published online by Cambridge University Press:  20 November 2018

G. C. Shephard
G. C. Shephard*
Affiliation:
University of East Anglia, Norwich, NOR 88C England
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Let S1 . . . ,Sr be r line segments, each of non-zero length, in n-dimensional euclidean space Rn. If a polytope Z is defined as the vector (Minkowski) sum

(1) Z = S1 + . . . + Sr,

then the segments Si will be called the components of Z. Since we do not wish to exclude the possibility that some of the components may be parallel, the polytope Z may be written in the form (1) in many different ways. For this reason it is convenient to define a zonotope to be the polytope Z together with some specified set of components {S1 , . . . , Sr}. Figures 1, 2 and 3 show some zonotopes of 1, 2 and 3 dimensions with 4, 5 and 6 components.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 2 , April 1974 , pp. 302 - 321
Copyright
Copyright © Canadian Mathematical Society 1974

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