  We compute phase diagrams for $A_nB_m$ starblock copolymers in the
strong-segregation regime as a function of volume fraction $\phi$, including
bicontinuous phases related to minimal surfaces (G, D, and P surfaces) as
candidate structures. We present the details of a general method to compute
free energies in the strong segregation limit, and demonstrate that the gyroid
G phase is the most nearly stable among the bicontinuous phases considered. We
explore some effects of conformational asymmetry on the topology of the phase
diagram.
