# 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.

## Linguistic Note

The plural of simplex is simplices, pronounced sim-pli-seez.

Compare the plural forms of vertex: vertices and index: indices.