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Identifying a polytope by its fibre polytopes

McMullen, P; (2020) Identifying a polytope by its fibre polytopes. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 10.1007/s13366-020-00527-2. Green open access

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Abstract

It is shown that a full-dimensional polytope P is uniquely determined by its r-dimensional fibre polytopes when r≥2. Further, if r≥4 and the r-dimensional fibre polytopes are zonotopes, then P itself must be a zonotope.

Type: Article
Title: Identifying a polytope by its fibre polytopes
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s13366-020-00527-2
Publisher version: https://doi.org/10.1007/s13366-020-00527-2
Language: English
Additional information: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Keywords: Polytope, fibre polytop, normal fan, zonotope
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/10117196
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