The beauty of E8

The E8 root system, or Gosset 421 polytope, is an exceptional uniform polytope in 8 dimensions, having 240 vertices and 6720 edges. This video shows a 2dimensional projection of this polytope as it rotates in various ways. The first 130 of the video show various small rotations of the polytope to illustrate some of its highly symmetric plane projections (at 10 we see a 30fold symmetry known as the Petrie figure, at 20 a 20fold symmetry, at 30 a 24fold symmetry, at 50 an 18fold symmetry and at