Combinatorial Rigidity of 3-dimensional Simplicial Polytopes
نویسندگان
چکیده
منابع مشابه
Triangulations of Simplicial Polytopes
Various facts about triangulations of simplicial polytopes, particularly those pertaining to the equality case in the generalized lower bound conjecture, are collected together here. They include an apparently weaker restriction on the kind of triangulation which needs to be found, and an inductive argument which reduces the number of cases to be established.
متن کاملMinimal Simplicial Dissections and Triangulations of Convex 3-Polytopes
This paper addresses three questions related to minimal triangulations of a three-dimensional convex polytope P. • Can the minimal number of tetrahedra in a triangulation be decreased if one allows the use of interior points of P as vertices? • Can a dissection of P use fewer tetrahedra than a triangulation? • Does the size of a minimal triangulation depend on the geometric realization of P? Th...
متن کاملA characterization of simplicial polytopes
Kalai proved that the simplicial polytopes with g2 = 0 are the stacked polytopes. We characterize the g2 = 1 case. Specifically, we prove that every simplicial d-polytope (d ≥ 4) which is prime and with g2 = 1 is combinatorially equivalent either to a free sum of two simplices whose dimensions add up to d (each of dimension at least 2), or to a free sum of a polygon with a (d− 2)-simplex. Thus,...
متن کاملClassification of pseudo-symmetric simplicial reflexive polytopes
Gorenstein toric Fano varieties correspond to so called reflexive polytopes. If such a polytope contains a centrally symmetric pair of facets, we call the polytope, respectively the toric variety, pseudo-symmetric. Here we present a complete classification of pseudo-symmetric simplicial reflexive polytopes. This is a generalization of a result of Ewald on pseudosymmetric nonsingular toric Fano ...
متن کاملGlobal rigidity of 3-dimensional cone-manifolds
We prove global rigidity for compact hyperbolic and spherical cone-3-manifolds with cone-angles ≤ π (which are not Seifert fibered in the spherical case), furthermore for a class of hyperbolic cone-3-manifolds of finite volume with cone-angles ≤ π, possibly with boundary consisting of totally geodesic hyperbolic turnovers. To that end we first generalize the local rigidity result contained in [...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2010
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnq143