On the Existence of Similar Sublattices
John H. Conway, Eric M. Rains, Neil J.A. Sloane · Canadian Journal of Mathematics · 1999
Abstract Partial answers are given to two questions. When does a lattice Λ contain a sublattice Λʹ of index N that is geometrically similar to Λ? When is the sublattice “clean”, in the sense that the boundaries of the Voronoi cells for Λʹ do not intersect Λ?