Simplex

Summary

An $n$-simplex is the convex hull of $n + 1$ points in general position, the simplest convex shape of dimension $n$. A point, a segment, a triangle and a tetrahedron are the simplices of dimensions $0$ to $3$. Simplices are the building blocks of simplicial complexes in topology and the cells of triangulations in geometry. Many notions of triangle geometry, such as the circumsphere and the centroid, extend to simplices.