The regular skew icosahedron is a six-dimensional regular polytope that is just as symmetric as the Platonic icosahedron,
but having different angles (Coxeter 1950; Coxeter 1999, pp. 143-145). A projection
of the regular skew icosahedron is depicted on the cover and on p. 144 of Coxeter
(1999).
Coxeter, H. S. M. "Self-Dual Configurations and Regular Graphs." Bull. Amer. Math. Soc.56, 413-455, 1950.Coxeter,
H. S. M. "Self-Dual Configurations and Regular Graphs." Reprinted
as Ch. 6 in The
Beauty of Geometry: Twelve Essays. New York: Dover, pp. 106-149, 1999.
