Examples of 'simplicial complex' in a sentence
Meaning of "simplicial complex"
simplicial complex: In mathematics, a simplicial complex is a structure formed by piecing together points, line segments, triangles, and their higher-dimensional counterparts in a specific way. It is used in the field of topology to study the properties of geometric shapes
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- A collection of simplices of various dimensions, connected to one another according to certain rules.
How to use "simplicial complex" in a sentence
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simplicial complex
We call such collection of objects a simplicial complex.
The elements of a simplicial complex are called the faces of that complex.
A class of simplices with this property is called a simplicial complex.
The dimension of a simplicial complex is defined as its maximum face dimension.
Note that the star is generally not a simplicial complex itself.
A simplicial complex that has a sequence of collapses leading to a point is called collapsible.
The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex.
An example is the chain complex defining the simplicial homology of a finite simplicial complex.
This link structure implies that the corresponding simplicial complex is necessarily a Euclidean building.
Strong collapse comprises of removal of special vertices called dominated vertices from a simplicial complex.
The processing effected for each input simplicial complex K is described below.
The simplicial Complex.
Determining whether the fundamental group of a finite simplicial complex is trivial.
How is a simplicial complex built from the data?
A topological space that is the polytope of a finite simplicial complex is called a polyhedron.
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Note that a simplicial complex is connected if and only if its 1-skeleton is connected.
A Delaunay triangulation is for us a simplicial complex.
This is a simplicial complex of dimension 1, and it can be colored by cotype.
Note that the star of S is generally not a simplicial complex itself.
Definitions = = A simplicial complex formula 1 is a set of simplices that satisfies the following conditions,,1.
There are compact 4-dimensional topological manifolds that are not homeomorphic to any simplicial complex.
Determining whether a finite simplicial complex is ( homeomorphic to ) a manifold.
Abstract, In this work we study the framework of mathematical morphology on simplicial complex spaces.
The fundamental group of a ( finite ) simplicial complex does have a finite presentation.
Condition 3 means that X is a strongly connected simplicial complex.
That is, it is a locally finite simplicial complex that covers the entire space.
Then the following conditions are equivalent, Vector f is the f-vector of a simplicial complex Δ.
Similarly, every simplex and every simplicial complex inherits a natural topology from Rn.
Condition 2 means that X is a non-branching simplicial complex.
C ( X ) is a simplicial complex.
Eduard Čech introduces the nerve construction, for associating a simplicial complex to an open covering.
For a deformable body represented by a finite simplicial complex K, the following solution is applicable,.
Let Δ { \ displaystyle \ Delta } be a finite or countably infinite simplicial complex.
For each face σ of each simplicial complex K,.
Vector f is the f-vector of a simplicial complex Δ.
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The dual of a simplicial polytope is called simple
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A simplicial polytope is a polytope whose facets are all simplices
