Polytopes

Definition

A polytope is the convex hull of a set of finitely many points.

An $m$-dimensional simplex is the convex hull of $m+1$ affinely independent points; an $m$-dimensional simplex is a polytope. The points are called the vertices of the simplex.

When $m = 0, 1, 2, 3$ the simplex is a point, closed line segment, triangle or tetrahedron.