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

Karim A. Adiprasito^*
, Arnau Padrol

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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

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Publisher Copyright:
© 2016, Hebrew University of Jerusalem.

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

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