Difference between revisions of "Link (geometry)"
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| − | In [[geometry]], the '''link''' of a vertex of a [[Two-dimensional space| | + | In [[geometry]], the '''link''' of a vertex of a [[Two-dimensional space|two-dimensional]] [[simplicial complex]] is a [[Graph (mathematics)|graph]] that encodes information about the local structure of the complex at the [[Vertex (geometry)|vertex]]. |
== Example == | == Example == | ||
Revision as of 05:33, 1 September 2015
In geometry, the link of a vertex of a two-dimensional simplicial complex is a graph that encodes information about the local structure of the complex at the vertex.
Example
The link of a vertex of a tetrahedron is a triangle -- the three vertices of the link corresponds to the three edges incident to the vertex, and the three edges of the link correspond to the faces incident to the vertex.
In this example, the link can be visualized by cutting off the vertex with a plane; formally, intersecting the tetrahedron with a plane near the vertex -- the resulting cross-section is the link.
TO DO - finish this section, provide image
Analog to sphere centered a point
A link is a graph-theoretic analog to a sphere centered at a point.
See also
- Geometry
- Graph (mathematics)
- Graph theory
- Simplicial complex
- Two-dimensional space
- Vertex (geometry)
External links
- Link (geometry) @ Wikipedia
