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Convex bodies equidecomposable by locally discrete groups of isometries

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

R. J. Gardner
R. J. Gardner
Affiliation:
University of Petroleum and Minerals, Department of Mathematical Sciences, Dhahran, Saudi Arabia.
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Abstract

We show that if a polytope K1, in ℝd can be partitioned into a finite number of sets, and these sets can be moved by isometries in a locally discrete group to form a convex body K2, then K2 is a polytope and a similar partition can be made where the sets involved are simplices with disjoint interiors. This gives partial answers to questions of Tarski, Sallee and Wagon.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 32 , Issue 1 , June 1985 , pp. 1 - 9
Copyright
Copyright © University College London 1985

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References

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