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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)

##### MSC:
 52B11 $$n$$-dimensional polytopes 52B12 Special polytopes (linear programming, centrally symmetric, etc.)
Full Text:
##### References:
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