  Deligne and Mostow constructed a class of lattices in PU(2,1) using monodromy
of hypergeometric functions. Later, Thurston reinterpreted them in terms of
cone metrics on the sphere. In this spirit we construct a fundamental domain
for all lattices with three fold symmetry in Deligne-Mostow list. This is a
generalisation of the works of Parker and Boadi and gives a different
interpretation of the fundamental domain constructed by Deraux, Falbel and
Paupert for some of these lattices.
