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Notes on the Plates

In: The Fifty-Nine Icosahedra

Author

Listed:
  • H. S. M. Coxeter
  • P. Du Val
  • H. T. Flather
  • J. F. Petrie

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.

Suggested Citation

  • H. S. M. Coxeter & P. Du Val & H. T. Flather & J. F. Petrie, 1982. "Notes on the Plates," Springer Books, in: The Fifty-Nine Icosahedra, chapter 4, pages 18-26, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8216-4_4
    DOI: 10.1007/978-1-4613-8216-4_4
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