The design of functional polymeric materials with tunable response requires a synergetic use of macromolecular architecture and interactions. Here, we combine experiments with computer simulations to demonstrate how physical properties of gels can be tailored at the molecular level, using star block copolymers with alternating block sequences as a paradigm. Telechelic star polymers containing attractive outer blocks self-assemble into soft patchy nanoparticles, whereas their mirror-image inverted architecture with inner attractive blocks yields micelles. In concentrated solutions, bridged and interpenetrated hexagonally packed nanocylinders are formed, respectively, with distinct structural and rheological properties. The phase diagrams exhibit a peculiar re-entrance where the hexagonal phase melts upon both heating and cooling because of solvent-block and block-block interactions. The bridged nanostructure is characterized by similar deformability, extended structural coherence, enhanced elasticity, and yield stress compared to micelles or typical colloidal gels, which make them promising and versatile materials for diverse applications.