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Angle-sum relations for polyhedral sets

Published online by Cambridge University Press:  26 February 2010

Peter McMullen
Peter McMullen
Affiliation:
Department of Mathematics, University College, Gower Street, London. WC1E 6BT
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Abstract

The Brianchon-Gram and Sommerville theorems on angle-sums for convex polytopes and polyhedral cones are here shown to be particular cases of an angle-sum relation for general polyhedral sets. The new relation is proved on the level of an equidissectability theorem, and this approach yields yet other angle-sum relations, including a different generalization of the Brianchon-Gram theorem. Further results extend, again to equidissections, earlier angle-sum relations of the author and others.

Type
Research Article
Information
Mathematika , Volume 33 , Issue 2 , December 1986 , pp. 173 - 188
Copyright
Copyright © University College London 1986

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