Hydrate networks are "host" lattices for the storage of "guest" natural gases. To enhance their physical stabilities near ambient conditions, the most stable clathrate hydrates should be identified. Here we report the towest-energy networks of the tetrakaidecahedral cage (T-cage) (H2O)(24) cluster, a constituent of the unit cell of the structure I [denoted (sl)] hydrate. A four-step screening method was employed to search for the towest-energy T-cage networks, which were eventually optimized at the MP2 level of theory. We further outline a procedure based on the obtained tow-energy isomers of the T-cage for constructing periodic unit cells of the (sl) hydrate lattice.