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Prodsimplicial-neighborly polytopes. (English) Zbl 1223.52005
From the abstract: The authors generalize simultaneously both neighborly and neighborly cubical polytopes to PSN polytopes: their \(k\)-skeleton is combinatorially equivalent to that of a product of \(r\) simplices. They construct PSN polytopes by three different methods, the most versatile of which is an extension of the “projecting deformed products” construction by R. Sanyal and G. M. Ziegler [Discrete Comput. Geom. 43, No. 2, 412–435 (2010; Zbl 1192.52019)] to products of arbitrary simple polytopes. For general \(r\) and \(k\), the lowest dimension they achieve is \(2k+r+1\). The authors show that this dimension is minimal if additionally required that the PSN polytope is obtained as a projection of a polytope that is combinatorially equivalent to the product of \(r\) simplices, when the dimensions of these simplices are all large compared to \(k\).
Reviewer: Eike Hertel (Jena)

52B11 \(n\)-dimensional polytopes
52B12 Special polytopes (linear programming, centrally symmetric, etc.)
Full Text: DOI arXiv
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