17 citations · 73 across the 26 of their papers we have counts for
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math.MG2014★ 3 cited
Universality theorems for inscribed polytopes and Delaunay triangulations
Karim A. Adiprasito, Arnau Padrol, Louis Theran
We prove that every primary basic semialgebraic set is homotopy equivalent to the set of inscribed realizations (up to Möbius transformation) of a polytope. If the semialgebraic se…
math.MG2014
Polygons as sections of higher-dimensional polytopes
Arnau Padrol, Julian Pfeifle
We show that every heptagon is a section of a -polytope with vertices. This implies that every -gon with can be obtained as a section of a $(2+\lfloor\frac{n}{7…
math.MG2014
The universality theorem for neighborly polytopes
Karim A. Adiprasito, Arnau Padrol
In this note, we prove that every open primary basic semialgebraic set is stably equivalent to the realization space of an even-dimensional neighborly polytope. This in particular…