Description:
<jats:title>Abstract</jats:title><jats:p>Even though a lattice and its sublattices have the same group of coincidence isometries, the coincidence index of a coincidence isometry with respect to a lattice Λ<jats:sub>1</jats:sub>and to a sublattice Λ<jats:sub>2</jats:sub>may differ. Here, we examine the coloring of Λ<jats:sub>1</jats:sub>induced by Λ<jats:sub>2</jats:sub>to identify how the coincidence indices with respect to Λ<jats:sub>1</jats:sub>and to Λ<jats:sub>2</jats:sub>are related. This leads to a generalization of the notion of color symmetries of lattices to what we call color coincidences of lattices. Examples involving the cubic and hypercubic lattices are given to illustrate these ideas.</jats:p>