4 papers · 1 filter
General non-realizability certificates for spheres with linear programming
Joao Gouveia, Antonio Macchia, Amy Wiebe
In this paper we present a simple technique to derive certificates of non-realizability for an abstract polytopal sphere. Our approach uses a variant of the classical algebraic cer…
Slack Ideals in Macaulay2
Antonio Macchia, Amy Wiebe
Recently Gouveia, Thomas and the authors introduced the slack realization space, a new model for the realization space of a polytope. It represents each polytope by its slack matri…
Combining realization space models of polytopes
João Gouveia, Antonio Macchia, Amy Wiebe
In this paper we examine four different models for the realization space of a polytope: the classical model, the Grassmannian model, the Gale transform model, and the slack variety…
Projectively unique polytopes and toric slack ideals
João Gouveia, Antonio Macchia, Rekha R. Thomas +1
The slack ideal of a polytope is a saturated determinantal ideal that gives rise to a new model for the realization space of the polytope. The simplest slack ideals are toric and h…