Multiple CSLs for the body centered cubic lattice

Ordinary Coincidence Site Lattices (CSLs) are defined as the intersection of a lattice Γ with a rotated copy RΓ of itself. They are useful for classifying grain boundaries and have been studied extensively since the mid sixties. Recently the interests turned to so-called multiple CSLs, i.e. intersections of n rotated copies of a given lattice Γ, in particular in connection with lattice quantizers. Here we consider multiple CSLs for the 3-dimensional body centered cubic lattice. We discuss the spectrum of coincidence indices and their multiplicity, in particular we show that the latter is a multiplicative function and give an explicit expression of it for some special cases.