A combination of detailed magnetisation studies and electronic-structure analysis using broken-symmetry DFT is used to explore the electronic structure of a trigonal prismatic Cu(II)(6) cluster. The presence of six paramagnetic metal centres with S = 1/2 gives rise to a maximum multiplicity of S = 3 and a total of 31 broken-symmetry states with M(S) < 3. Computed differences in energy between the high-spin and broken-symmetry states are expressed in terms of the 15 distinct Heisenberg exchange coupling parameters, J(ij), and the equations are solved by a least-squares fitting procedure. By inspection of the errors introduced by progressive symmetrisation of the Hamiltonian to reduce the number of independent J(ij), we arrive at a minimal model containing only four distinct J(ij) (three intra- and one inter-triangular). The computed values then guide the fitting of the magnetisation data. The computed trends in J(ij) can only be reproduced when antisymmetric exchange is included in the model Hamiltonian. The use of this Hamiltonian provides a reasonable description of the magnetic behaviour at all temperatures and fields. If a simpler isotropic model Hamiltonian is used instead, the best fit values of J(ij) are compromised by the need to fit the low-temperature region where antisymmetric exchange dominates the shape of the curve.