Israel Journal of Mathematics

, Volume 211, Issue 1, pp 239–255 | Cite as

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

  • Karim A. Adiprasito
  • Arnau Padrol


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.


Unique Point Projective Transformation Combinatorial Type Projective Basis Oriented Matroid 
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Copyright information

© Hebrew University of Jerusalem 2016

Authors and Affiliations

  1. 1.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance
  2. 2.Institut für MathematikFU BerlinBerlinGermany

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