TY - JOUR
T1 - A universality theorem for projectively unique polytopes and a conjecture of Shephard
AU - Adiprasito, Karim A.
AU - Padrol, Arnau
N1 - Publisher Copyright:
© 2016, Hebrew University of Jerusalem.
PY - 2016/2/1
Y1 - 2016/2/1
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.
UR - http://www.scopus.com/inward/record.url?scp=84953339841&partnerID=8YFLogxK
U2 - 10.1007/s11856-015-1272-7
DO - 10.1007/s11856-015-1272-7
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AN - SCOPUS:84953339841
SN - 0021-2172
VL - 211
SP - 239
EP - 255
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -