A permutohedron is a pictorial representation of all the permutations a set of objects can form. Permutohedron of two pens would be a line, of tree pens would be a triangular prism.

1. A permutohedron (pictured below left) is a pictorial representation of all the permutations a set of objects can form. The permutohedron of two pens would be a line, of tree pens would be a triangular prism (most famously a Toblerone, pictured below right). In math language, permutohedron of order n has n! vertices adjacent to n-1 others with total number of edges equal to (n-1)n!/2. Each edge has a length of root 2.