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Reconstruction of polytopes by convex pastings

Part of: Polytopes and polyhedra

Published online by Cambridge University Press:  26 February 2010

Gabriele H. Greco  and
Charles D. Horvath
Gabriele H. Greco
Affiliation:
Dipartimento di Matematica, Università di Trento, 38050 Povo, Italy. E-mail: [email protected]
Charles D. Horvath
Affiliation:
Département de Mathématiques, Université de Perpignan, 66860 Perpignan cedex, France, E-mail: [email protected]
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Abstract

Consider a convex polytope X and a family of convex sets, satisfying a given property P. Moreover, assume that is closed under operations of cutting and convex pasting along hyperplanes. Necessary and sufficient conditions are given to have . As a consequence, it follows that, if all simplices or small enough simplices have the property in question, then X also has that property.

MSC classification

Secondary: 52B11: $n$-dimensional polytopes
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 9 - 18
Copyright
Copyright © University College London 2000

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References

1.Brøndsted, A.. An Introduction to Convex Polytopes (Springer, New York, 1983).CrossRefGoogle Scholar
2.Flām, S. D. and Greco, G. H.. Minimax and intersection theorems. In Fixed Point Theory and Applications (Théra, M. A. and Baillon, J. B., eds.), Longman Scientific and Technical (1991), 123–140.Google Scholar
3.Greco, G. H.. Minimax theorems and saddling transformations. J. Math. Anal. Appl., 147 (1990), 180–197.CrossRefGoogle Scholar
4.Grünbaum, B.. Convex Polytopes. (Wiley-Interscience, London, 1967).Google Scholar