# 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 vertices have the same length.