Simplex
From Wikipedia, the free encyclopedia
Jump to:
navigation,
search
For other uses, see Simplex (disambiguation).
A 3-simplex or
tetrahedron
In
geometry, a
simplex (plural
simplexes or
simplices) or
n-simplex is an
n-dimensional analogue of a triangle. Specifically, a simplex is the
convex hull of a set of (
n + 1)
affinely independent points in some
Euclidean space of dimension
n or higher (i.e., a set of points such that no
m-
plane contains more than (
m + 1) of them; such points are said to be in
general position).For example, a 0-simplex is a
point, a 1-simplex is a
line segment, a 2-simplex is a
triangle, a 3-simplex is a
tetrahedron, and a 4-simplex is a
pentachoron (in each case with interior).A
regular simplex is a simplex that is also a
regular polytope. A regular
n-simplex may be constructed from a regular (
n − 1)-simplex by connecting a new vertex to all original vertices by the common edge length.