Notes on the Plates

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

Chapter 4 in The Fifty-Nine Icosahedra, 1982, pp 18-26 from Springer

Abstract: Abstract The Icosahedron A needs no comment. B is obtained by erecting low triangular pyramids (b) on each face of A, and is thus what we may call (by analogy with cristallographic terminology) a triakisicosahedron, save that the edges of A are concave, not convex, edges of B. C is the figure of five octahedra, dual to that of five cubes; each of the twenty planes contains a face each of two of these octahedra (the face of C is in fact clearly a pair of crossed triangles); and for each of the ten possible pairs out of the five octahedra a pair of opposite faces of one are coplanar respectively with a pair of opposite faces of the other, this accounting just for the ten pairs of opposite faces of the icosahedron. D has two sets of pits or depressions, 20 whose cross section (or vertex figure) is a triangle, and 12 of which it is a pentagram.

Keywords: Plate Versus; Vertex Figure; Pentagonal Pyramid; Narrow Wedge; Enantiomorphous Form (search for similar items in EconPapers)
Date: 1982
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DOI: 10.1007/978-1-4613-8216-4_4

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