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Symmetrical sets of constant width and their partitions

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

C. A. Rogers
C. A. Rogers
Affiliation:
University College, London.
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Extract

In this note we shall be mainly concerned with convex bodies of constant width in En that are invariant under the group of congruences that leave invariant a regular simplex with its centre of gravity at the origin. We first show that there are many such convex bodies. This follows, by showing that any set S ot diameter 1 that is invariant under a group of congruences about the origin, is contained in a convex body of constant width 1 that is invariant under the group.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)

Information

Type
Research Article
Information
Mathematika , Volume 18 , Issue 1 , June 1971 , pp. 105 - 111
Copyright
Copyright © University College London 1971

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References

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