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The E_8 root system, or Gosset 4_21 polytope, is an exceptional uniform polytope in 8 dimensions, having 240 vertices and 6720 edges. This video shows a 2-dimensional projection of this polytope as it rotates in various ways. The first 1′30″ of the video show various small rotations of the polytope to illustrate some of its highly symmetric plane projections (at 10″ we see a 30-fold symmetry known as the Petrie figure, at 20″ a 20-fold symmetry, at 30″ a 24-fold symmetry, at 50″ an 18-fold symmetry and at
