TOPICS
An 
polytope is a polytope
having the symmetry of the exceptional simple Lie groups 
of dimension 248. There are 255 uniform polytopes with 
symmetry in 8 dimensions. The simplest
of these are summarized in the following table.
| polytope | vertex count |
 | 240 |
 | 2160 |
 | 17280 |
The graph corresponding to the skeleton of 
(also called the 
root polytope) is implemented in Wolfram
Language as GraphData["421PolytopeGraph"].
." 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 
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.
Weisstein, Eric W. "E_8 Polytope." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/E8Polytope.html