M Theory Lesson 58
Higher dimensional analogues of the hexagon polytope are known as permutohedra, because they describe permutations on $(d + 1)$ letters. Loday showed that by cutting hypercubes with hyperplanes one can naturally obtain both associahedra and then permutohedra in any dimension. Postnikov et al have done a lot of work on the combinatorics of generalised permutohedra.
As a shameless thief of pretty pictures, today I offer the reader the $6_3$ knot on the Klein surface! A six punctured Klein surface has a moduli space of real dimension 24, which is a number we like a lot.