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In geometry, a simplex ( plural simplexes or simplices ) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension.

Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices.

For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, and a 4-simplex is a pentachoron.

A single point may be considered a 0-simplex, and a line segment may be considered a 1-simplex.

A simplex may be defined as the smallest convex set containing the given vertices.