Icosahedral coincidence rotations

Abstract

Abstract The coincidence problem for three-dimensional discrete structures with icosahedral symmetry is reinvestigated. We present a parametric description of the coincidence rotations based on special quaternions, called icosian numbers. In particular, we give a characterization of the possible coincidence indices (Σ-factors) and present a complete list of the possible rotations with Σ < 50.