- Title
- On the reconstruction of polytopes
- Creator
- Doolittle, Joseph; Nevo, Eran; Pineda-Villavicencio, Guillermo; Ugon, Julien; Yost, David
- Date
- 2019
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/168068
- Identifier
- vital:13772
- Identifier
-
https://doi.org/10.1007/s00454-018-9997-9
- Identifier
- ISBN:0179-5376
- Abstract
- Blind and Mani, and later Kalai, showed that the face lattice of a simple polytope is determined by its graph, namely its 1-skeleton. Call a vertex of a d-polytope nonsimple if the number of edges incident to it is more than d. We show that (1) the face lattice of any d-polytope with at most two nonsimple vertices is determined by its 1-skeleton; (2) the face lattice of any d-polytope with at most d- 2 nonsimple vertices is determined by its 2-skeleton; and (3) for any d> 3 there are two d-polytopes with d- 1 nonsimple vertices, isomorphic (d- 3) -skeleta and nonisomorphic face lattices. In particular, the result (1) is best possible for 4-polytopes. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
- Publisher
- Springer New York LLC
- Relation
- Discrete and Computational Geometry Vol. 61, no. 2 (2019), p. 285-302. http://purl.org/au-research/grants/arc/DP180100602
- Rights
- Copyright © 2018, Springer Science+Business Media, LLC, part of Springer
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; 0103 Numerical and Computational Mathematics; 0802 Computation Theory and Mathematics; k-Skeleton; Reconstruction; Simple polytope
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