An order 4 permutohedron.

Quoting Wikipedia, “In mathematics, the permutohedron of order *n* (also spelled permutahedron) is an (*n* − 1)-dimensional polytope embedded in an *n*-dimensional space, the vertices of which are formed by permuting the coordinates of the vector (1, 2, 3, …, *n*). More generally, the term describes any polyhedron which is the convex hull of a free orbit of the symmetric group S_{n} acting naturally on R^n. The edge-graph of any permutohedron is the Cayley graph of S_{n} with respect to the generating set of adjacent transpositions (1,2), … , (*n* − 1,*n*).”

Mathematics is beautiful. <3