Triangular hyperbolic buildings

Abstract

We construct triangular hyperbolic polyhedra whose links are generalized 4-gons. The universal cover of such a polyhedron is a hyperbolic building, whose apartments are hyperbolic planes tessellated by regular triangles with angles π / 4 . The fundamental groups of the polyhedra are hyperbolic, torsion free, with property (T). To cite this article: R. Kangaslampi, A. Vdovina, C. R. Acad. Sci. Paris, Ser. I 342 (2006).