This polytope lies in the 8-dimensional space. Its 1-skeleton consists of 240 vertices and 6720 edges. What we see here is the Petrie projection onto the Coxeter plane displaying a wonderful rotational symmetry of order 30. The 240 vertices are distributed in 8 concentric circles of 30 vertices each, where all vertices in the same circle are connected by straight lines, except the diametrically opposed. 

The vertices provide a solution of the kissing number as well as best packing of 7-dimensional spheres. The Lie group E8 occurs in theoretical physics, more precisely in string theory and supergravity. More information is available at http://topologia. wordpress.com/2010/10/10/e8-con-hilo-tensado/