Constructions arborescentes d'immeubles

Abstract.

 We prove that, contrarily to the case of spherical and euclidean buidings, the set of (isomorphism classes of) locally finite 3-dimensional hyperbolic buildings is uncountable. The proof uses on one hand a classification of 3-dimensional Coxeter polytops satisfying some local properties of irreducibility and symmetry, and on another hand, an arborescent construction of buildings for splitable Coxeter systems.