Deforming the RR-Fuchsian (4, 4, 4)-triangle group into a lattice

We prove that the last discrete deformation of the RR-Fuchsian (4, 4, 4)-triangle group in PU(2,1)PU(2,1) is a cocompact arithmetic lattice. We also describe an experimental method for finding the combinatorics of a Dirichlet fundamental domain, and apply it to the lattice in question.