Non-positively curved triangles of finite groups are of cohomological dimension 2 over the rationals and have Property FA. We classify triangles of finite groups which satisfy certain geometric conditions including the Gauss--Bonnet theorem. We investigate whether or not these groups are virtually torsion-free, contain a free abelian subgroup of rank 2, are residually finite or are linear.
"Platonic triangles of groups." Experiment. Math. 7 (3) 191 - 219, 1998.