justify this phase have failed in both the strong segregation limit, where Fredrickson chose a catenoid as a candidate base surface;[@fredrickson91] and in the weak-segregation limit by self-consistent field calculations [@MatsBate96]. Recent experiments [@hajdukunpub] have shown that the HPL phase is not an equilibrium phase in diblock melts, but may be metastable.

Here we present the calculations of Ref. [@olmsted94a] in more detail. We show that the G geometry is the most stable of the candidate bicontinuous phases, followed by the D and P geometries, and that the G phase can be stable for block-copolymers with sufficient conformational asymmetry. The outline of this paper is as follows. In Section \[sec:general\] we present the formalism for calculating the free energy in general geometries. In Section \[sec:classical\] we present the results for the classical diblock topologies (lamellae, cylinders, and spheres), extended to include non-round unit cells and, in the case of the cylindrical topology, kinked paths. In Section \[sec:bicontinuous\] we present the free energy for a generic “saddle” wedge, which is representative of a generic bicontinuous structure as a pie-shaped wedge is representative of cylindrical phases regardless of packing. We then introduce the geometry necessary for calculating the free energy of the 