# Permutohedron

The first few permutohedra are the point (order 1), line segment (order 2), regular hexagon (order 3), truncated octahedron (order 4), great prismatodecachoron (order 5), and great cellidodecateron (order 6). In fact the nth-order permutohedron is (a variant of) the (n-1)-dimensional omnitruncated simplex and has n! vertices, (n - 1) n! / 2 edges, and ${\displaystyle (n - d)! \left\{{n \atop n - d}\right\}}$ facets of rank d where the curly braces denote the Stirling numbers of the second kind.