’ s repository of research publications and other research outputs Coincidence rotations of the root lattice

The coincidence site lattices of the root lattice A4 are considered, and the statistics of the corresponding coincidence rotations according to their indices is expressed in terms of a Dirichlet series generating function. This is possible via an embedding of A4 into the icosian ring with its rich arithmetic structure, which recently [6] led to the classification of the similar sublattices of A4. Dedicated to Ludwig Danzer on the occasion of his 80th birthday