Simplex (EntityClass, 14)
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| - | A '''simplex''' is an n-dimensional [[polytope]] with n+1 faces and n+1 vertices. | + | A '''simplex''' is an n-dimensional regular [[polytope]] with n+1 faces and n+1 vertices. |
Simplices are special because they are always [[convex]] and are never [[self-intersecting]]. Any polytope can also be built out of simplices of its own dimension. For these reasons, simplices are often used as "building blocks" in [[CGI]]. | Simplices are special because they are always [[convex]] and are never [[self-intersecting]]. Any polytope can also be built out of simplices of its own dimension. For these reasons, simplices are often used as "building blocks" in [[CGI]]. | ||
Revision as of 18:26, 17 June 2007
A simplex is an n-dimensional regular polytope with n+1 faces and n+1 vertices.
Simplices are special because they are always convex and are never self-intersecting. Any polytope can also be built out of simplices of its own dimension. For these reasons, simplices are often used as "building blocks" in CGI.
Simplices are all also self-duals. The only other regular polytope to exhibit this behavior, bar 2D shapes, is the icositetrachoron in 4D.
Template:Generalization-dimensions
