Simplex

An $n$-simplex is the simplest possible polytope (convex hull) of $n+1$ points in $n$-dimensional space, where the points are affinely independent.

Examples:

• 0-simplex: A point (1 vertex).
• 1-simplex: A line segment (2 vertices).
• 2-simplex: A triangle (3 vertices).
• 3-simplex: A tetrahedron (4 vertices).