Simplex (EntityClass, 14)
From Hi.gher. Space
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Simplices are special because they are always [[convex]] and are never [[self-intersecting]]. Any polytope can be defined as the union of a set of simplices of its own dimension, or as the space bounded by the union of a set of simplices of one dimension less. 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 be defined as the union of a set of simplices of its own dimension, or as the space bounded by the union of a set of simplices of one dimension less. For these reasons, simplices are often used as "building blocks" in [[CGI]]. | ||
| - | + | Regular simplices are all also self-[[dual]]s. The only other regular polytope to exhibit this behavior, bar 2D shapes, is the [[icositetrachoron]] in 4D. | |
{{generalization-dimensions|[[Triangle]] • [[Tetrahedron]] • [[Pentachoron]] • [[Hexateron]]}} | {{generalization-dimensions|[[Triangle]] • [[Tetrahedron]] • [[Pentachoron]] • [[Hexateron]]}} | ||
Revision as of 16:11, 21 November 2009
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 be defined as the union of a set of simplices of its own dimension, or as the space bounded by the union of a set of simplices of one dimension less. For these reasons, simplices are often used as "building blocks" in CGI.
Regular 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
