Representations of polytopes and polyhedral sets
Representations of polytopes and polyhedral sets
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多面体和多面体集的表示
DOI：
10.1007/bf00149284
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发表时间：
1973
影响因子：
0.5
通讯作者：
P. McMullen
中科院分区：
文献类型：
--
作者：
P. McMullen;P. McMullen
本文描述了图技术的一种变体，如多面体的Gale图和正基的正图，它们适用于多面体集。我们得到了多面体或多面体集合的平移不变表示。这种方法自然会导致对熟悉的组合图关系的更简单的证明。然而，这种方法比以前使用的方法更通用，因为它可以用于研究多面体集的线性系统，以及体积等度量性质。特别地，我们给出了Meyer关于多面体可分解性的一个结果的简单证明，并给出了闵可夫斯基关于多面体可实现性的著名定理的一个更清晰的方法，该多面体的面片给出了外法向量和外面积。
In this paper we describe a variant of the diagram techniques, such as Gale diagrams for polytopes and positive diagrams for positive bases, which is appropriate for polyhedral sets. We obtain our new technique as a translation-invariant representation of polytopes or polyhedral sets. This approach leads naturally to simpler proofs of the familiar combinatorial diagram relationships. However, this method is more versatile than those previously employed, in that it can be used to investigate linear systems of polyhedral sets, and metrical properties such as volume. In particular, we give an easy proof of a result of Meyer on decomposability of polytopes, and a more perspicuous way of looking at the well-known theorem of Minkowski on the realizability of polytopes whose facets have given outer normal vectors and areas.