and locally specified the volume fraction per molecule,[@olmsted94a; @Miln94; @Miln94b], while Likhtman and Semenov relaxed the assumption of straight paths [@LikhSeme94] but enforced the constraint of constant $\phi$ per molecule only globally. The former approach corresponds to an upper bound on the free energy (see below), while it is not clear that the Likhtman-Semenov calculations corresponds to any bound, or indeed to any systematic approximation, because the local constraint of constant composition is relaxed. By comparing upper bounds between bicontinuous, C, and L phases (obtained for the cylindrical phase by assuming hexagonal symmetry and imposing straight paths), we showed that the bicontinuous phases are unstable, when comparing upper bounds, to the L and C phases. Later, Xi and Milner extended this work to calculations with kinked polymer paths, and found an upper bound to the hexagonal phase which lies very close to the lower bound using round unit cells.[@XiMiln96b]

Experiments have found an additional phase at $\chi$ values between the G and L phases [@hamley93], a hexagonally-perforated lamellae (HPL) phase, which consists of majority lamellae connected through a minority matrix by hexagonal arrays of tubes.[@disko93] The stacking has been suggested to be $ABCABC$ [@Fors+94] or $ABAB$ [@hamley93]. Theoretical attempts to 