The ground-state properties of a Co3II moiety encapsulated in a polyoxometalate anion were investigated by combining measurements of specific heat, magnetic susceptibility, and low-temperature magnetization with a detailed inelastic neutron scattering (INS) study on a fully deuterated polycrystalline sample of Na12[Co3W(D2O)2(ZnW9O34)2].40D2O (Co3). The ferromagnetic Co3O14 cluster core consists of three octahedrally oxo-coordinated CoII ions. According to the single-ion anisotropy and spin-orbit coupling of the octahedral CoII ions, the appropriate exchange Hamiltonian to describe the ground-state properties of the Co3 spin cluster is anisotropic and is expressed as H = -2 sigma a = x,y,z (Ja12 S1a S2a + Ja23 S2a S3a), where Ja are the components of the exchange interactions between the CoII ions. To reproduce the INS data, different orientations of the two anisotropic J tensors must be considered, and the following conditions had to be introduced: Jx12 = Jy23, Jy12 = Jx23, Jz12 = Jz23. This result was correlated with the molecular symmetry of the complex. The following set of parameters was obtained: Jx12 = Jy23 = 1.37, Jy12 = Jx23 = 0.218, and Jz12 = Jz23 = 1.24 meV. This set also reproduces in a satisfactory manner the specific heat, susceptibility, and magnetization properties of Co3.