A universality theorem for projectively unique polytopes and a conjecture of Shephard
Metric Geometry
2013-06-14 v2 Combinatorics
Abstract
We prove that every polytope described by algebraic coordinates is the face of a projectively unique polytope. This provides a universality property for projectively unique polytopes. Using a closely related result of Below, we construct a combinatorial type of 5-dimensional polytope that is not realizable as a subpolytope of any stacked polytope. This disproves a classical conjecture in polytope theory, first formulated by Shephard in the seventies.
Keywords
Cite
@article{arxiv.1301.2960,
title = {A universality theorem for projectively unique polytopes and a conjecture of Shephard},
author = {Karim Alexander Adiprasito and Arnau Padrol},
journal= {arXiv preprint arXiv:1301.2960},
year = {2013}
}
Comments
9 pages, 6 figures; both main results substantially improved and generalized