In the presence of a midblock-selective solvent, triblock copolymers not only self-organize but also form a molecular network. Thermoplastic elastomer gels constitute examples of such materials and serve as sealants and adhesives, as well as ballistic, microfluidic, and electroactive media. We perform Monte Carlo and dissipative particle dynamics simulations to investigate the phase behavior and network characteristics of these materials. Of particular interest is the existence of a truncated octahedral morphology that resembles the atomic arrangement of various inorganic species. Both simulation approaches quantify the midblock bridges responsible for network development and thus provide a detailed molecular picture of these composition-tunable soft materials.