J. Phys. Colloques
Volume 47, Numéro C3, Juillet 1986International Workshop on Aperiodic Crystals
|Page(s)||C3-165 - C3-172|
J. Phys. Colloques 47 (1986) C3-165-C3-172
THE ICOSAHEDRAL ORIENTATION MANIFOLD AS A MODEL FOR ICOSAHEDRAL CLOSE-PACKINGF.C. FRANK
HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, GB-Bristol BS8 1TL, Great Britain
Geometrical mappings of the orientation manifold for icosahedral symmetry, both by means of Rodrigues vectors and Quaternion parameter vectors are described. In such mappings the set of 60 points representing the same orientation as the point at the origin provide an array with spherically cyclic closure, in which each point of the array has, topologically, the same icosahedral environment as every other : in which, moreover, the configuration of points in an inner region makes a tolerably good match to the configuration of a low energy packing of 33 or even 45 atoms : so providing a directly visualizable model of an ideal icosahedral close-packing.