4-Simplex

As I learned from topology, a 0-simplex is a point. A 1-simplex is a line (two points oriented). A 2-simplex is a triangle (three points oriented). A 3-simplex is a tetrahedron (4 points oriented). In each of these simplexes, every point is connected to every other point, and the simplex can be filtrated down into smaller simplexes (using the boundary function). The 0-3 simplexes are usually depictable in handwriting. The 4-simplex, or, five points oriented, meaning 5 tetrahedrons connected (without any holes, so a loop) in 4D space.