We give an explicit construction of a family of lattices in PU (1, 2) originally constructed by Livné. Following Thurston, we construct these lattices as the modular group of certain Euclidean cone metrics on the sphere. We give connections between these groups and other groups of complex hyperbolic isometries.
"Cone metrics on the sphere and Livné’s lattices." Acta Math. 196 (1) 1 - 64, 2006. https://doi.org/10.1007/s11511-006-0001-9