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Decomposable convex polyhedra

Published online by Cambridge University Press:  26 February 2010

G. C. Shephard
G. C. Shephard
Affiliation:
University of Birmingham.
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Extract

By a convex polyhedron P we mean any bounded set which can be written as the intersection of a finite number of closed half-spaces. If P can be written as a vector sum Q+B of convex polyhedra, then Q and B are called summands of P. If P has a summand which is not homothetic to itself, then P is said to be decomposable.

Type
Research Article
Information
Mathematika , Volume 10 , Issue 2 , December 1963 , pp. 89 - 95
Copyright
Copyright © University College London 1963

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References

1.Bonnesen, T and Fenchel, W, Theorie der Konvexen Körpe, (New York, 1948).Google Scholar
2.Gale, D., “Irreducible convex sets”, Proc. I.C.M., Amsterdam, 1954 II, 217–218.Google Scholar
3.Grünbaum, B., “Measures of symmetry of convex sets”, Proc. Symposia Pure Math, 7 (1963), 233–270.CrossRefGoogle Scholar