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Fibre tilings

McMullen, P; (2003) Fibre tilings. MATHEMATIKA , 50 (1-2) 1 - 33. 10.1112/S0025579300014765. Green open access

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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.

Type: Article
Title: Fibre tilings
Open access status: An open access version is available from UCL Discovery
DOI: 10.1112/S0025579300014765
Publisher version: http://dx.doi.org/10.1112/S0025579300014765
Language: English
Additional information: © 2003 Cambridge University Press
Keywords: CELL-COMPLEXES, POLYTOPES, ZONOTOPES, POLYHEDRA, DUALITY
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/104968
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