The Weyl group of C4

Time for a pretty picture! It's the Weyl group of the finite Lie algebra C₄.

Although C₄ is 'only' 36 dimensional, its Weyl group is a bit bigger and has 384 elements. The pictures doesn't show the elements of the Weyl group though, but rather all possible connections between them. If you looks closely the black dots aren't dots -- they're points where are lots of lines meet.