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E_8 Polytope


An E_8 polytope is a polytope having the symmetry of the exceptional simple Lie groups E_8 of dimension 248. There are 255 uniform polytopes with E_8 symmetry in 8 dimensions. The simplest of these are summarized in the following table.

polytopevertex count
4_(21)240
2_(41)2160
1_(42)17280

The graph corresponding to the skeleton of 4_(21) (also called the E_8 root polytope) is implemented in Wolfram Language as GraphData["421PolytopeGraph"].


See also

600-Cell, Polytope

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References

Baez, J. C. "From the Icosahedron to E_8." 21 Dec 2017 . https://arxiv.org/abs/1712.06436.Baez, J. C. "The Icosidodecahedron." 26 Sep 2023. https://arxiv.org/abs/2309.15774.Dechant, P.-P. "The Birth of E_8 Out of the Spinors of the Icosahedron." Proc. Roy. Soc. A 472, 20150504, 2016.Conway, J. H. and Sloane, N. J. A. Sphere Packings, Lattices, and Groups, 2nd ed. New York: Springer-Verlag, 1993.Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, 1973.Coxeter, H. S. M. Kaleidoscopes: Selected Writings of H. S. M. Coxeter (Ed. F. A. Sherk, P. McMullen, A. C. Thompson, and A. I. Weiss). New York: Wiley, 1995.Johnson, N. W. The Theory of Uniform Polytopes and Honeycombs. Ph.D. Dissertation. Toronto, Canada: University of Toronto, 1966.

Cite this as:

Weisstein, Eric W. "E_8 Polytope." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/E8Polytope.html

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