Visualizing the E_{8} root systemThe E_{8} root system consists of 240 vectors in an eightdimensional space. See what is E_{8}? Those vectors are the vertices (corners) of an eightdimensional object called the Gosset polytope 4_{21}. In the 1960s, Peter McMullen drew (by hand) a 2dimensional representation of the Gosset polytope 4_{21}. The image shown below was computergenerated by John Stembridge, based on McMullen's drawing.The lines in the picture connect adjacent vertices in the polytope, with colors chosen according to the length of the 2dimensional projection. Since the picture is a 2dimensional projection of an 8dimensional object, it captures only some of the symmetries of the Gossett polytope. We thank John H. Conway, mathematics professor at Princeton University, for pointing out to us the connection between E_{8} and the Gosset polytope 4_{21}. The Lie algebra E_{8} is 248dimensional: the 8dimensional space depicted here, plus one dimension for each of the 240 root vectors. Picture also available as a high resolution EPS file or PDF file. A scan of a copy of Peter McMullen's drawing available as a 300 dpi PDF (2 Meg). Please contact AIM if you know the location of McMullen's original drawing of the Gosset polytope 4_{21}.
For more details about Coxeter planes and pictures of root systems, see John Stembridge's web page. More information about E_{8} and the Gossett polytope, and a 3dimensional Zome model, can be found on David Richter's website.
