## Simplex

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

*k*-dimensional polytope which is the convex hull of its

*k*+ 1 vertices. More formally, suppose the

*k*+ 1 points are affinely independent, which means are linearly independent. Then, the simplex determined by them is the set of points . 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.

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