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Approximations by polytopes with projectively regular facets

Published online by Cambridge University Press:  26 February 2010

G. C. Shephard
G. C. Shephard
Affiliation:
University of Washington, Seattle, U.S.A. and University of Birmingham, England
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Extract

It is well known that every convex polytope in d-dimensional euclidean space Ed can be approximated arbitrarily closely, in the Hausdorff sense, by convex polytopes whose faces are simplexes (see [2, Section 4.5]). In this paper we prove some generalizations of this result, investigating the possibility of approximating a given d-polytope (d-dimensional convex polytope) by polytopes whose facets (faces of d − 1 dimensions) are all of some prescribed type.

Type
Research Article
Information
Mathematika , Volume 13 , Issue 2 , December 1966 , pp. 189 - 195
Copyright
Copyright © University College London 1966

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References

1. Coxeter, H. S. M., Regular polytopes (New York 1948, second edition, 1963).Google Scholar
2. Grünbaum, B., Convex polytopes (Wiley and Sons, to be published soon).Google Scholar
3. Hodge, W. V. D. and Pedoe, D., Methods of algebraic geometry (Cambridge, 1947).Google Scholar