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- Title
Around A. D. Alexandrov's uniqueness theorem for convex polytopes.
- Authors
Panina, Gaiane
- Abstract
Two dependent examples are presented: 1. Two convex polytopes in R³ 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 S² 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.
- Subjects
UNIQUENESS (Mathematics); CONVEX polytopes; PARALLELS (Geometry); TRIANGULARIZATION (Mathematics); REGULAR graphs; GEOMETRICAL constructions; POLYTOPES
- Publication
Advances in Geometry, 2012, Vol 12, Issue 4, p621
- ISSN
1615-715X
- Publication type
Article
- DOI
10.1515/advgeom-2012-0006