A universality theorem for projectively unique polytopes and a\n conjecture of Shephard

2013/01/14 by Karim Adiprasito, Adiprasito, Karim Alexander, Arnau Padrol +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1301.2960

Abstract

We prove that every polytope described by algebraic coordinates is the face\nof a projectively unique polytope. This provides a universality property for\nprojectively unique polytopes. Using a closely related result of Below, we\nconstruct a combinatorial type of 5-dimensional polytope that is not realizable\nas a subpolytope of any stacked polytope. This disproves a classical conjecture\nin polytope theory, first formulated by Shephard in the seventies.\n

Cited by

• Many projectively unique polytopes
• Antiprismless, or: Reducing Combinatorial Equivalence to Projective Equivalence in Realizability Problems for Polytopes

Related

• An Algebraic Approach to Projective Uniqueness with an Application to\n Order Polytopes
• Many projectively unique polytopes
• Antiprismless, or: Reducing Combinatorial Equivalence to Projective Equivalence in Realizability Problems for Polytopes
• Quotients of a Universal Locally Projective Polytope of type 5,3,5
• The universality theorem for neighborly polytopes