mathematics, the subdivision of simplicial sets (subdivision functor or Sd functor) is an endofunctor on the category of simplicial sets. It refines the...

A subdivision (also called refinement) of a simplicial complex is another simplicial complex in which, intuitively, one or more simplices of the original...

for weak homotopy equivalences. Using the subdivision of simplicial sets, the extension of simplicial sets is defined as: Ex : s S e t → s S e t , Ex...

the edges by paths Subdivision (simplicial complex) Subdivision (simplicial set) Subdivision surface, in computer graphics Subdivision, an administrative...

mathematics, the barycentric subdivision is a standard way to subdivide a given simplex into smaller ones. Its extension to simplicial complexes is a canonical...

In mathematics, a simplicial complex is a structured set composed of points, line segments, triangles, and their n-dimensional counterparts, called simplices...

A simplicial map (also called simplicial mapping) is a function between two simplicial complexes, with the property that the images of the vertices of...

In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by...

topological properties of simplicial complexes and their generalizations, cell-complexes. An abstract simplicial complex above a set V {\displaystyle V} is...

topological data analysis, a subdivision bifiltration is a collection of filtered simplicial complexes, typically built upon a set of data points in a metric...

small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space...

implementation typically involves four steps: coordinate skewing, simplicial subdivision, gradient selection, and kernel summation. An input coordinate is...

is an abstract simplicial complex (that is, a family of finite sets closed under the operation of taking subsets), formed by the sets of vertices in the...

a locally finite simplicial complex that covers the entire space. A point-set triangulation, i.e., a triangulation of a discrete set of points P ⊂ R d...

standard in the Solar System In geometry, Barycentric subdivision, a way of dividing a simplicial complex Barycentric coordinates (mathematics), coordinates...

illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory...

Simplex Simplicial complex Polytope Triangulation Barycentric subdivision Simplicial approximation theorem Abstract simplicial complex Simplicial set Simplicial...

lemma Polytope Simplex Simplicial complex CW complex Manifold Triangulation Barycentric subdivision Sperner's lemma Simplicial approximation theorem Nerve...

In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and...

subdivision and the extension, providing a connection with the category of simplicial sets itself. The constructions include the join of simplicial sets...

(barycentric subdivision, dual triangulation), Poincaré lemma, the first proof of the general Stokes Theorem, and a lot more L. E. J. Brouwer: simplicial approximation...

the trivial topology). When subdividing simplicial complexes (the first barycentric subdivision of a simplicial complex is a refinement), the situation...

representation and processing, in geometrical modeling, they are related to simplicial set and to combinatorial topology, and this is a boundary representation...

definition of "orbihedron", the simplicial analogue of an orbifold. Let X be a finite simplicial complex with barycentric subdivision X '. An orbihedron structure...

dimension of each flag. Namely, the barycentric subdivision of a simplicial complex is the abstract simplicial complex defined using flags of simplices in...

g-conjecture on the possible numbers of faces of different dimensions in a simplicial sphere (also Grünbaum conjecture, several conjectures of Kühnel) (Karim...

The upper bound theorem states that if Δ {\displaystyle \Delta } is a simplicial sphere of dimension d − 1 {\displaystyle d-1} with n {\displaystyle n}...

the subdivision, plus all the incidence and adjacency relations between these cells. When all the represented cells are simplexes, a simplicial complex...

field. Tits demonstrated how to every such group G one can associate a simplicial complex Δ = Δ(G) with an action of G, called the spherical building of...

graph we may associate an abstract simplicial complex C with a single-element set per vertex and a two-element set per edge. The geometric realization...