Simplex
In geometry, a simplex (plural: simplices or simplexes), sometimes called n-simplex is the n-dimensional analogue figure of the triangle. A triangle is a 2-simplex. The 0-simplex is the point, the 1-simplex is the line segment (line connecting two points). The 3-simplex is the tetrahedron, and the 4-simplex is the pentachoron.
A regular simplex is a simplex that is also a regular polytope. A regular n-simplex may be made from a regular (n - 1)-simplex by connecting a new vertex to all the other vertices. All the edges have the same length.
Simplex Media
The four simplexes that can be fully represented in 3D space.
The numbers of faces in the above table are the same as in Pascal's triangle, without the left diagonal.
The total number of faces is always a power of two minus one. This figure (a projection of the tesseract) shows the centroids of the 15 faces of the tetrahedron.
en:1-simplex family graph, in A1 Coxeter plane
en:2-simplex family graph, in A2 Coxeter plane
3-simplex graph in A3 Coxeter plane
4-simplex graph
en:5-simplex family polytope graph, in A5 Coxeter plane
en:6-simplex family graph in A6 Coxeter plane
uniform 7-polytope graph*Public domainPublic domainfalsefalse*
