  All three-dimensional matter-free spacetimes with negative cosmological
constant, compatible with cyclic symmetry are identified. The only cyclic
solutions are the 2+1 (BTZ) black hole with SO(2) x R isometry, and the
self-dual Coussaert-Henneaux spacetimes, with isometry groups SO(2) x SO(2,1)
or SO(2) x SO(2).
