(\vec{R}-\vec{r})\over |\vec{R} - \vec{r}|^2}
\right]\end{aligned}$$ and similarly for $d\vec{R}'$. Remarkably, the upper bound for the kinked-path-hexagonal ansatz is typically less than $1\%$ above the lower bound of cylindrical micelles, and the transition is shifted to only a slightly smaller $A$ fraction $\phi$ (see Figure \[fig:classicalb\]). Apparently the extra stretching energy to maintain a hexagonal $A\!-\!B$ interface with straight paths is relaxed considerably by allowing the inner block to adopt a more nearly circular dividing surface, which is preferred. Recent accurate numerical self-consistent field calculations of diblock melts have shown that in fact the $A\!-\!B$ interface is nearly circular, with a slight hexagonal modulation (angular modulation with 6-fold symmetry) of relative amplitude $0.03\%$ at $\chi N= 60$ and $\phi=0.33$ [@matsen97].

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Geometry of bicontinuous phases {#sec:bicontinuous}
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Generic saddle surfaces {#sec:wedge}
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Before addressing particular symmetries (P, D, or G) of bicontinuous phases, we discuss the closest analogue to a round unit cell. We would like to produce a simple estimate of the free energy, analogous to the cylindrical and spherical micelle calculation, which captures the physics of bicontinuous topologies. We thus represent a generic bicontinuous phase as a wedge, shown in Figure \[fig:chip\]: an infinitesimal patch of “saddle” surface, with 