  We classify all the symmetric integer bilinear forms of signature (2,1) whose
isometry groups are generated up to finite index by reflections. There are 8595
of them up to scale, whose 374 distinct Weyl groups fall into 39
commensurability classes. This extends Nikulin's enumeration of the strongly
square-free cases. Our technique is an analysis of the shape of the Weyl
chamber, followed by computer work using Vinberg's algorithm and our "method of
bijections". We also correct a minor error in Conway and Sloane's definition of
their canonical 2-adic symbol.
