Optimization of the reaction of [Ln(hfac)(3)]center dot 2H(2)O and pyridine-N-oxide (PyNO), which is known to afford double-bridged dimers, leads to triple-bridged dimers of formula [(Ln(hfac)(3))(2)(PyNO)(3)] (Ln = Gd (1), Dy (2)) from which the Dy derivative (2) behaves as a single-molecule magnet (SMM). The pseudo threefold axis symmetry of this zero-dimensional building block makes possible its extension into a tridimensional network. By changing PyNO for 4,4'-bipyridine N,N'-dioxide (4,4'BipyNO) a tridimensional compound of formula {[Ln(hfac)(3)](2)(4,4'BipyNO)(2)]} (Ln = Eu (3), Gd (4), and Dy (5)) is then rationally obtained. This covalent three-dimensional (3D) network has a remarkably high cell volume (V = 24 419 A(3)) and is an arrangement of interpenetrated 3D subnetworks whose triple-bridged dimers still behave as SMMs.