Varying the length of poly(dimethylsiloxane) in poly(cyclohexylethylene-b-ethylene-b-cyclohexylethylene-b-dimethylsiloxane) (CECD) block terpolymers between 0 and 20% produces the sequence of ordered phases: cylindrical-to-network-to-cylindrical. Small-angle X-ray scattering and transmission electron microscopy demonstrate Pnna space group symmetry and a unique network morphology stabilized by the asymmetric molecular architecture and block interactions. These results establish a new design principle for the generation of triply periodic and multiply continuous nano-structured soft materials.