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Reuleaux polytopes

Published online by Cambridge University Press:  26 February 2010

G. T. Sallee
G. T. Sallee
Affiliation:
Department of Mathematics, The University of California, Davis, California, U.S.A.
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Extract

All of our work takes place in Ed, d-dimensional Euclidean space, with unit ball B. Unless specifically noted to the contrary, all sets will be presumed to be closed and convex. If X is a subset of a sphere S with centre p, we will say X is spherically convex if X is contained in some open hemisphere of S and if the cone generated by X with vertex p is convex. The distance between two points x, y ε Ed will be denoted |x − y|. If K1K2 are two convex sets, ρ(K1, K2) will mean the usual Hausdorff distance between them.

Type
Research Article
Information
Mathematika , Volume 17 , Issue 2 , December 1970 , pp. 315 - 323
Copyright
Copyright © University College London 1970

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References

1.Eggleston, H. G., Convexity (Cambridge University Press, Cambridge, 1958).CrossRefGoogle Scholar
2.Eggleston, H. G., “Sets of constant width in finite dimensional Banach spaces”, Israel J. Math., 3 (1968), 163–172.CrossRefGoogle Scholar
3.Sallee, G. T., “The maximal set of constant width in a lattice”, Pacific J. Math., 28 (1969), 669–674.CrossRefGoogle Scholar
4.Yaglom, I. M. and Boltyanskii, W. G., Convex figures, English Translation (Holt, Rinehart and Winston, 1961).Google Scholar