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We describe a general approach to constructing small free Z -resolutions for certain infinite isometry groups . We apply the method to a class of generalized triangle groups and use the resolution to compute the integral homology of these groups. In illustrating the method we also obtain resolutions for the classical triangle groups and for their infinite cyclic central extensions, considered previously by Strebel. (2000) . 20J06, 30F40, 57M60. Mathematics Subject Classification of thedoi:10.4171/cmh/26 fatcat:oaoi2aczm5bcrnbqpcbl2psheu