Stochastic explorations of the structural possibilities of neutral WC6 clusters in several spin states lead to very rich and complex potential energy surfaces, with geometries quite different from those of pure carbon clusters at the PBEO/def2-TZVP level. The global minimum is predicted to be a triplet-state semicyclic C-6 conformation having every carbon in direct coordination to the W atom. Interaction energies are comparable to those of C-7 clusters, revealing very strong W-C bonding. Our results suggest that C-C interactions in the clusters should be considered as intermediate between single and double bonds.