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Type cones and products of simplices

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Speaker: Bennet Goeckner (Univ. of Washington)


Abstract: A polytope PPP is the convex hull of finitely many points in Euclidean space. For polytopes PPP and QQQ, we say that QQQ is a Minkowski summand of PPP if there exists some polytope RRR such that Q+R=PQ+R=PQ+R=P. The type cone of PPP encodes all of the (weak) Minkowski summands of P. In general, combinatorially isomorphic polytopes can have different type cones. We will first consider type cones of polygons, and then show that if PPP is combinatorially isomorphic to a product of simplices, then the type cone is simplicial. No previous knowledge of polytopes will be assumed. This is joint work with Federico Castillo, Joseph Doolittle, Michael Ross, and Li Ying.

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