  A periodic lattice in Euclidean 3-space is the infinite set of all integer
linear combinations of basis vectors. Any lattice can be generated by
infinitely many different bases. This ambiguity was only partially resolved,
but standard reductions remained discontinuous under perturbations modelling
crystal vibrations. This paper completes a continuous classification of
3-dimensional lattices up to Euclidean isometry (or congruence) and similarity
(with uniform scaling).The new homogeneous invariants are uniquely ordered
square roots of scalar products of four superbase vectors whose sum is zero and
all pairwise angles are non-acute. These root invariants continuously change
under perturbations of basis vectors. The geometric methods extend the work of
Delone, Conway and Sloane.
