6.AT.4. UNIFORM POLYHEDRA
H. S. M. Coxeter, M. S. Longuet Higgins & J. C. P. Miller. Uniform polyhedra. Philos. Trans. Roy. Soc. 246A (1954) 401 450. They sketch earlier work and present 53 uniform polyhedra, beyond the 5 Platonic, 13 Archimedean and 4 Kepler Poinsot polyhedra and the prisms and anti prisms. Three of these uniform polyhedra are actually infinite families. "... it is the authors' belief that the enumeration is complete, although a rigorous proof has still to be given."
S. P. Sopov. Proof of completeness of the list of uniform polyhedra. Ukrain. Geometr. Sb. 8 (1970) 139-156. ??NYS -- cited in Skilling, 1976.
J. S. Skilling. The complete set of uniform polyhedra. Philos. Trans. Roy. Soc. London Ser. A 278 (1975) 111 135. Demonstrates that the 1954 list of Coxeter, et al., is complete. If one permits more than two faces to meet at an edge, there is one further polyhedron -- the great disnub dirhombidodecahedron.
J. S. Skilling. Uniform compounds of uniform polyhedra. Math. Proc. Camb. Philos. Soc. 79 (1976) 447-468. ??NYS -- I am told it determines that there are 75 uniform compounds and also cites Sopov.
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