Coincidence rotations of the root lattice $A_4$

Abstract

The coincidence site lattices of the root lattice $A_4$ 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 $A_4$ into the icosian ring with its rich arithmetic structure, which recently (arXiv:math.MG/0702448) led to the classification of the similar sublattices of $A_4$.

13 pages, 1 figure

References in corpus (2)

• A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns
• Coincidence site modules in 3-space

Cited by in corpus (3)

• A Note on Coincidence Isometries of Modules in Euclidean Space
• Similar Sublattices and Coincidence Rotations of the Root Lattice A4 and its Dual
• Ten colours in quasiperiodic and regular hyperbolic tilings