Planes and rows in icosahedral quasilattices

(Revised 8 December 1992, accepted in final form 9 March 1993)

Abstract
The planar and linear substructures of a threedimensional icosahedral Ammann-Kramer-Penrose quasilattice have been analysed. Infinitely many families of planes and rows are existing such that each family covers all vertices of the quasilattice. The members of a family of parallel planes are separated by at least three but a finite number of different distances, whose sequence is quasiperiodic and can be uniquely characterized by a strip-projection method from a two-dimensional periodic lattice. The same is valid for the sequence of vertices on each row. The vertex pattern in each single plane results from a strip-projection from 2 + 2 dimensions. In addition to several specific patterns we have determined the vertex occupation densities of planes and rows and their statistics. The families of planes with highest occupation densities correspond well to minima of backscattering profiles, which have been calculated in numerical simulation of heavy ion-channeling in the primitively decorated quasilattice.