2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/27749The 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 (Sigma-factors) and present a complete list of the possible rotations with Sigma < 100.A version with abbreviated tables will occur in Z.KristCondensed Mattertext