We compute phase diagrams for A(n)B(m) starblock copolymers in the str
ong-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 demonstra
te that the gyroid G phase is the most nearly stable among the biconti
nuous phases considered. We explore some effects of conformational asy
mmetry on the topology of the phase diagram.