Definition:Simplex

Definition
A simplex is an $n$-dimensional generalization of a triangle and tetrahedron, for $n \in \Z_{>0}$.

A $k$-simplex is a $k$-dimensional polytope which is the convex hull of its $k + 1$ vertices.

Also see

 * Equivalence of Definitions of Simplex


 * Definition:Pentatope