  We explicitly compute the lower algebraic K-theory of the split
three-dimensional crystallographic groups; i.e., the groups G that act properly
and cocompactly on three-dimensional Euclidean space by isometries, such that
the natural map from G to O(3) is a split injection onto its image. There are
73 split three-dimensional crystallographic groups in all, out of a total of
219 isomorphism types of three-dimensional crystallographic groups.
  We also provide a general splitting formula for the lower algebraic K-theory
that is valid for all three-dimensional crystallographic groups. This result
generalizes earlier work of Alves and Ontaneda.
  Along the way, we give explicit descriptions of all 73 split
three-dimensional crystallographic groups, and completely work out their
classification. The split crystallographic groups are sometimes called
"splitting groups". A theorem of crystallographic groups says that any
crystallographic group is a finite-index subgroup of its splitting group, so
each three-dimensional crystallographic group is a finite-index subgroup of one
from our list.
