منابع مشابه
New polytopes from products
We construct a new 2-parameter family Emn, m, n ≥ 3, of self-dual 2-simple and 2-simplicial 4-polytopes, with flexible geometric realisations. E44 is the 24-cell. For large m, n the f -vectors have “fatness” close to 6. The Et-construction of Paffenholz and Ziegler applied to products of polygons yields cellular spheres with the combinatorial structure of Emn. Here we prove polytopality of thes...
متن کاملProducts of abstract polytopes
Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polytopes and introduce a new product, called the topological product, which also arises in a natural way. We show that these products have unique prime factorization theorems. We use this to compute the automorphism group ...
متن کاملProducts of polytopes and inequalities
The cd-index is a polynomial which encodes the ag f-vector of a convex polytope. We determine explicit recurrences for computing the cd-index of the free join U _ V of two polytopes U and V and the cd-index of the Cartesian product U V. As an application of these recurrences, we prove the inequality (U _ (V W)) ((U _ V) W) involving the cd-indices of three polytopes.
متن کاملDeformed Products and Maximal Shadows of Polytopes
We present a construction of deformed products of polytopes that has as special cases all the known constructions of linear programs with \many pivots," starting with the famous Klee-Minty cubes from 1972. Thus we obtain sharp estimates for the following geometric quantities for d-dimensional simple polytopes with at most n facets: the maximal number of vertices on an increasing path, the maxim...
متن کاملGorenstein Fano Polytopes Arising from Order Polytopes and Chain Polytopes
Richard Stanley introduced the order polytope O(P ) and the chain polytope C(P ) arising from a finite partially ordered set P , and showed that the Ehrhart polynomial of O(P ) is equal to that of C(P ). In addition, the unimodular equivalence problem of O(P ) and C(P ) was studied by the first author and Nan Li. In the present paper, three integral convex polytopes Γ(O(P ),−O(Q)), Γ(O(P ),−C(Q...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2006
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2005.12.008