Complete Enumeration of Stellated Icosahedra, by Considering the Possible Faces

H. S. M. Coxeter, P. Du Val, H. T. Flather and J. F. Petrie

Chapter 2 in The Fifty-Nine Icosahedra, 1982, pp 8-14 from Springer

Abstract: Abstract The eighteen straight lines in Fig. 3 (analogous to Fig. 1)* show how the plane of any one face 0 of the icosahedron is met by the planes of eighteen other faces (namely, all the other faces except the opposite one). The lines PP′, QQ′, RR′, SS′, TT′, UU′ are typical, in the sense that the rest can be derived from these six by rotations through ±2/3π. The faces whose planes make these intersections are marked p, q, r, s, t, u, in Fig. 2. Note that pairs of opposite faces (p, u; q, t; r, s) lead to pairs of parallel lines.

Keywords: Common Part; Complete Enumeration; Icosahedral Symmetry; Trigonal Symmetry; Rotational Sense (search for similar items in EconPapers)
Date: 1982
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DOI: 10.1007/978-1-4613-8216-4_2

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