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 journalArticlepeer-review

3 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 languageAmerican English
Pages (from-to)239-255
Number of pages17
JournalIsrael Journal of Mathematics
Volume211
Issue number1
DOIs
StatePublished - 1 Feb 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016, Hebrew University of Jerusalem.

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