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Reducible convex sets

Published online by Cambridge University Press:  26 February 2010

G. C. Shephard
G. C. Shephard
Affiliation:
Department of Mathematics, The University of Washington, Seattle, Washington.
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Let H be any closed bounded convex set in En, and -H be its reflection in the origin. Then the vector sum K = H+ (−H) has the origin as centre and is called the difference set of H. Clearly every closed bounded convex set K with centre at the origin is the difference set of ½K. Excluding this trivial case, we define such a set K to be reducible if it is the difference set of some H which is not homothetic to K.

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Type
Research Article
Information
Mathematika , Volume 13 , Issue 1 , June 1966 , pp. 49 - 50
Copyright
Copyright © University College London 1966

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References

1. Coxeter, H. S. M., Regular polytopes (New York and Chicago, 1947).Google Scholar
2. Grünbaum, B., “On a conjecture of H. Hadwiger”, Pacific J. of Math., 11 (1961), 215–219.CrossRefGoogle Scholar
3. Shephard, G. C., “Decomposable convex polyhedra”, Mathematika, 10 (1963), 89–95.CrossRefGoogle Scholar