Water clusters are formed in helium droplets via the sequential capture of monomers. One or two neon atoms are added to each droplet prior to the addition of water. The infrared spectrum of the droplet ensemble reveals several signatures of polar, water tetramer clusters having dipole moments between 2D and 3D. Comparison with ab initio computations supports the assignment of the cluster networks to noncyclic "3 + 1" clusters, which are similar to 5.3 kcal/mol less stable than the global minimum nonpolar cyclic tetramer. The (H2O)(3)Ne + H2O ring insertion barrier is sufficiently large, such that evaporative helium cooling is capable of kinetically quenching the nonequilibrium tetramer system prior to its rearrangement to the lower energy cyclic species. TO this end; the reported process results in the formation of exotic water cluster networks that are either higher in energy than the most stable gas-phase analogs or not even stable in the gas phase.