  Generic wave dislocations (phase singularities, optical vortices) in three
dimensions have anisotropic local structure, which is analysed, with emphasis
on the twist of surfaces of equal phase along the singular line, and the
rotation of the local anisotropy ellipse (twirl). Various measures of twist and
twirl are compared in specific examples, and a theorem is found relating the
(quantised) topological twist and twirl for a closed dislocation loop with the
anisotropy C line index threading the loop.
