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A functional analytic interpretation of the number of faces of a polyhedron

Part of: Polytopes and polyhedra

Published online by Cambridge University Press:  26 February 2010

Krzysztof Przesławski
Krzysztof Przesławski
Affiliation:
Instytut Matematyki, Uniwersytet Zielonogórski, ul. Podgórna 50, 65–246, Zielona Góra, Poland. E-mail: k.przeslawski@im.pz.zgora.pl
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Extract

Let P⊂ℝ2 be a polyhedron, that is, the intersection of a finite number of closed half-spaces, and suppose that its characteristic function lP can be expressed as a linear combination

where each Ai is a relatively open and convex set. Let n(P) be the number of all non-empty facets of P. One of the main objectives of this paper is to show that

MSC classification

Secondary: 52B05: Combinatorial properties (number of faces, shortest paths, etc.)
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 1 - 7
Copyright
Copyright © University College London 2000

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References

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