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

Karim A. Adiprasito; Arnau Padrol

doi:10.1007/s11856-015-1272-7

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

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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.

Original language	English
Pages (from-to)	239-255
Number of pages	17
Journal	Israel Journal of Mathematics
Volume	211
Issue number	1
DOIs	https://doi.org/10.1007/s11856-015-1272-7
State	Published - 1 Feb 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-015-1272-7

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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.",

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N2 - 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.

AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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