edges given by the normals, terminating in a small line segment lying along the bond-lattice. We envision the surface as a minimal surface, which has zero mean curvature.[@nitsche]

The stretching free energy per molecule of the symmetric wedge can be calculated as before, given the relative area as a function of relative height along the center normal (Table \[table1\]): $a(\lambda)\!=\!\lambda(2-\lambda)$, where $\lambda\!=\!z/R$, $z\!=\!0$ is the thin end of the wedge and $z\!=\!R$ is the patch of minimal surface. As before, the dividing surface location $z_d$ is determined by eq \[eq:zdloc\]. The resulting free energy is given by applying eqs \[eq:zdloc\]-\[eq:interf\], and is shown with the various cylindrical bounds in Figure \[fig:classicalb\]. This estimate misses by a few tenths of one percent the intersection of the lamellar phase and the kinked-path upper bound bound for the hexagonal phase, and is stable with respect to the straight-path upper bound.

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Clearly the simple wedge construction captures some important physics. The structures formed by copolymers at different volume fractions $\phi$ arise from competition between interfacial and stretching free energies. The different structures present different functions $a(\lambda)$, which determine both the dividing surface area and the stretching energy as a function of volume fraction. 