Coincidence site modules in 3-space

Abstract

The coincidence site lattice (CSL) problem and its generalization to Z-modules in Euclidean 3-space is revisited, and various results and conjectures are proved in a unified way, by using maximal orders in quaternion algebras of class number 1 over real algebraic number fields.

25 pages

References in corpus (3)

• Planar coincidences for N-fold symmetry
• Solution of the coincidence problem in dimensions $d\le 4$
• Multiple planar coincidences with N-fold symmetry

Cited by in corpus (7)

• Solution of the coincidence problem in dimensions $d\le 4$
• Coincidence rotations of the root lattice $A_4$
• A Note on Coincidence Isometries of Modules in Euclidean Space
• Discrete Tomography of Icosahedral Model Sets
• Similarity and Coincidence Isometries for Modules
• The coincidence problem for shifted lattices and crystallographic point packings
• Discrete Tomography of F-Type Icosahedral Model Sets