  We give an algebro-geometric construction of some of the non-arithmetic ball
quotients constructed by the author, Parker and Paupert. The new construction
reveals a relationship between the corresponding orbifold fundamental groups
and the automorphism group of the Klein quartic, and also with groups
constructed by Barthel-Hirzebruch-H\"ofer and Couwenberg-Heckman-Looijenga.
