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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: greco@science.unitn.it
Charles D. Horvath
Affiliation:
Département de Mathématiques, Université de Perpignan, 66860 Perpignan cedex, France, E-mail: horvath@univ-perp.fr
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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

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