Around A. D. Alexandrov's uniqueness theorem for convex polytopes

被引：1
|
作者：
Panina, Gaiane [1 ]
机构：
[1] Inst Informat & Automat, St Petersburg 199178, Russia
来源：
ADVANCES IN GEOMETRY | 2012年 / 12卷 / 04期
关键词：
Pseudo triangulation; regular triangulation; convex polytope; virtual polytope; hyperbolic virtual polytope; PSEUDO-TRIANGULATIONS;
D O I：
10.1515/advgeom-2012-0006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Two dependent examples are presented: 1. Two convex polytopes in R-3 such that for each pair of their parallel facets, one of the facets fits strictly into the other. (The example gives a refinement of A. D. Alexandrov's uniqueness theorem for convex polytopes.) 2. A pointed tiling of the two-sphere S-2 generated by a Laman-plus-one graph which can be regularly triangulated without adding extra vertices. The construction uses the combinatorial rigidity theory of spherically embedded graphs and the relationship between the theory of pseudo triangulations and the theory of hyperbolic virtual polytopes.
引用
收藏
页码：621 / 637
页数：17
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