Coincidences of Hypercubic Lattices in 4 dimensions

We consider the CSLs of 4-dimensional hypercubic lattices. In particular, we derive the coincidence index $\mathrm{\Sigma }$ and calculate the number of different CSLs as well as the number of inequivalent CSLs for a given $\mathrm{\Sigma }$. The hypercubic face centered case is dealt with in detail and it is sketched how to derive the corresponding results for the primitive hypercubic lattice.