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Abstract: Simultaneously generalizing both neighborly and neighborly cubical polytopes,we introduce PSN polytopes: their k-skeleton is combinatorially equivalent tothat of a product of r simplices. We construct PSN polytopes by three differentmethods, the most versatile of which is an extension of Sanyal and Ziegler-s-projecting deformed products- construction to products of arbitrary simplepolytopes. For general r and k, the lowest dimension we achieve is 2k+r+1.Using topological obstructions similar to those introduced by Sanyal to boundthe number of vertices of Minkowski sums, we show that this dimension isminimal if we additionally require that the PSN polytope is obtained as aprojection of a polytope that is combinatorially equivalent to the product of rsimplices, when the dimensions of these simplices are all large compared to k.

Autor: Benjamin Matschke, Julian Pfeifle, Vincent Pilaud


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