  The chromatic number of a lattice in n-dimensional Euclidean space is defined
as the chromatic number of its Voronoi graph. The Voronoi graph is the Cayley
graph on the lattice having the strict Voronoi vectors as generators. In this
paper we determine the chromatic number of all 4-dimensional lattices. To
achieve this we use the known classification of 52 parallelohedra in dimension
4. These 52 geometric types yield 16 combinatorial types of relevant Voronoi
graphs. We discuss a systematic approach to checking for isomorphism of Cayley
graphs of lattices. Lower bounds for the chromatic number are obtained from
choosing appropriate small finite induced subgraphs of the Voronoi graphs.
Matching upper bounds are derived from periodic colorings. To determine the
chromatic numbers of these finite graphs, we employ a SAT solver.
