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The toroidal analogue to Eberhard's theorem

Published online by Cambridge University Press:  26 February 2010

Peter Gritzmann
Peter Gritzmann
Affiliation:
Math. Inst. Univ. Siegen, Hölderlinstrasse 3, D-5900 Siegen, Fed. Rep. Germany.
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Extract

In 1891 Victor Eberhard proved the following theorem concerning the number pk(P) of k-gonal facets of simple polytopes P, [4].

Eberhard's Theorem. For each k ≥ 3, k ≠ 6, let pk be a non-negative integer. Then there exists a simple 3-polytope P such that pk(P) = pk (k ≠ 6), if, and only if,

Type
Research Article
Information
Mathematika , Volume 30 , Issue 2 , December 1983 , pp. 274 - 290
Copyright
Copyright © University College London 1983

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