In mathematics, a **simplex** is the simplest possible type of polytope in any given dimension. More specifically, an *n*-simplex is the convex hull of its *n + 1* vertices that are affinely independent. For example, a 0-simplex is a point, a 1-simplex is a line segment, a 2-simplex is a triangle, and a 3-simplex is a tetrahedron.