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Fibre tilings

Part of: Discrete geometry

Published online by Cambridge University Press:  26 February 2010

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

Generalizing an earlier notion of secondary polytopes, Billera and Sturmfels introduced the important concept of fibre polytopes, and showed how they were related to certain kinds of subdivision induced by the projection of one polytope onto another. There are two obvious ways in which this concept can be extended: first, to possibly unbounded polyhedra, and second, by making the definition a categorical one. In the course of these investigations, it became clear that the whole subject fitted even more naturally into the context of finite tilings which admit strong duals. In turn, this new approach provides more unified and perspicuous explanations of many previously known but apparently quite disparate results.

MSC classification

Secondary: 52C22: Tilings in $n$ dimensions
Type
Research Article
Information
Mathematika , Volume 50 , Issue 1-2 , December 2003 , pp. 1 - 33
Copyright
Copyright © University College London 2003

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