The newly synthesized tetra(quinoline-TEMPO)yttrium(III) potassium salt shows interesting structural features at the molecular and supramolecular levels, revealed by the analysis of the X-ray diffraction data. The magnetic susceptibility and EPR data corroborated with structural considerations showed that the exchange and dipolar spin coupling interactions are taking place at the nodes assembling the supramolecular 2D structure. The Y(III) center shows antiprismatic octacoordination, close to the idealized D-2 symmetry. The diamagnetic transition metal plays no role in mediating the radical interactions since the TEMPO-type fragments are remote from the chelating moieties of the ligand. In turn, significant interaction occurs on the nodes consisting in the quasi-rectangular coordination of potassium counterions by the spin-bearing TEMPO groups coming from four distinct complex units. The antiferromagnetic susceptibility was consistently modeled by a spin Hamiltonian based on the rectangle topology of four spins S = (1)/(2). The fitted exchange parameters are J(a) = -5.1 cm(-1) and J(b) = -3.4 cm(-1) for the edges, imposing J(d) = 0 for the diagonal. These values are in excellent agreement with the ab initio results J(a) = -4.83 cm(-1), J(b) = -3.44 cm(-1), J(d) = -0.07 cm(-1) obtained in a CASSCF(12,8) calculation. Based on the reliability of the ab initio results we were able to select the presented J parameters among several versions of multiple solutions with acceptable goodness of the fit. A methodological caveat about the artifacts of the automatic use of best fit parameters, in the absence of supplementary criteria, in the context of relative blindness of magnetic susceptibility modeling, is raised. The details of the EPR spectrum at 10 K are also consistent, in the frame of dipolar approximation, with the model of four interacting spins at the nodes of the supramolecular assembling.