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# simplicial complex

A collection of simplices of various dimensions, connected to one another according to certain rules.

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• Simplicial complex — In mathematics, a simplicial complex is a topological space of a particular kind, constructed by gluing together points, line segments, triangles, and their n dimensional counterparts (see illustration). Simplicial complexes should not be… …   Wikipedia

• Abstract simplicial complex — In mathematics, an abstract simplicial complex is a purely combinatorial description of the geometric notion of a simplicial complex, consisting of a family of finite sets closed under the operation of taking subsets. In the context of matroids… …   Wikipedia

• Simplicial homology — In mathematics, in the area of algebraic topology, simplicial homology is a theory with a finitary definition, and is probably the most tangible variant of homology theory. Simplicial homology concerns topological spaces whose building blocks are …   Wikipedia

• Simplicial sphere — In geometry and combinatorics, a simplicial (or combinatorial) d sphere is a simplicial complex homeomorphic to the d dimensional sphere. Some simplicial spheres arise as the boundaries of convex polytopes, however, in higher dimensions most… …   Wikipedia

• Complex — A complex is a whole that comprehends a number of intricate parts, especially one with interconnected or mutually related parts; for example, a complex of buildings. Complex may refer to: Contents 1 Biology 2 Chemistry …   Wikipedia

• Simplicial manifold — In mathematics, the term simplicial manifold commonly refers to either of two different types of objects, which combine attributes of a simplex with those of a manifold. Briefly; a simplex is a generalization of the concept of a triangle into… …   Wikipedia

• Simplicial polytope — A d dimensional simplicial polytope is a polytope whose facets are adjacent to exactly d ridges.They are topologically dual to simple polytopes. Polytopes which are bothsimple and simplicial are either simplices or two dimensional polygons.… …   Wikipedia

• Simplicial approximation theorem — In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by a slight deformation) approximated by ones that are piecewise of the simplest kind. It applies… …   Wikipedia

• Clique complex — “Whitney complex” redirects here. For the Mississippi sports facility, see Davey Whitney Complex. Clique complexes, flag complexes, and conformal hypergraphs are closely related mathematical objects in graph theory and geometric topology that… …   Wikipedia

• Vietoris–Rips complex — In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is an abstract simplicial complex that can be defined from any metric space M and distance delta; by forming a simplex for every finite set of points that… …   Wikipedia