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Space-filling zonotopes

Published online by Cambridge University Press:  26 February 2010

G. C. Shephard
G. C. Shephard
Affiliation:
University of East Anglia, Norwich NR4 7TJ, England.
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Extract

By a zonotope we mean any set in Euclidean n-dimensional space Rn which can be written as a Minkowski (vector) sum of a finite number of line segments. A zonotope is a convex centrally-symmetric polytope, and all its faces are zonotopes. Familiar examples of three-dimensional zonotopes include the cube, rhombic dodecahedron, elongated dodecahedron (Figure 1) and truncated octahedron. Photographs of models of more complicated examples appear in [1, Plate II].

Type
Research Article
Information
Mathematika , Volume 21 , Issue 2 , December 1974 , pp. 261 - 269
Copyright
Copyright © University College London 1974

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References

1.Coxeter, H. S. M.. Regular Polytopes (London-New York 1948, Second edition, 1963, Third edition, 1973).Google Scholar
2.Coxeter, H. S. M.. “The classification of zonohedra by means of projective diagrams”, J. Math. pures appliquées 41 (1962), 137–156; reprinted in Twelve Geometric Essays, (Illinois-London-Amsterdam, 1968).Google Scholar
3.McMulIen, P.. “On zonotopes”, Trans. American Math. Soc., 159 (1971), 91–109.CrossRefGoogle Scholar
4.Shephard, G. C.. “Combinatorial properties of associated zonotopes”, Canadian J. Math., 26 (1974), 302–321.CrossRefGoogle Scholar