  An entirely new and independent enumeration of the crystallographic space
groups is given, based on obtaining the groups as fibrations over the plane
crystallographic groups, when this is possible. For the 35 ``irreducible''
groups for which it is not, an independent method is used that has the
advantage of elucidating their subgroup relationships. Each space group is
given a short ``fibrifold name'' which, much like the orbifold names for
two-dimensional groups, while being only specified up to isotopy, contains
enough information to allow the construction of the group from the name.
