this in practice we use the following procedure. For cylindrical micelles we divide a cell of a given symmetry (say, hexagonal) into tiny wedges. Each wedge is adjusted slightly by making the segment of the wedge on the dividing surface normal to the bisector of the wedge, which is the path of the polymer. Such an adjustment introduces a negligible volume in the continuum limit of many small wedges. The surface area used for calculating the surface energy (eq \[eq:Sa\]) is, of course, the area of the segment in the original hexagonal dividing surface (before adjusting the wedge to account for straight paths).

=3.5truein

For the classical phases (see Figure \[fig:classicala\]) the ratios of the upper and lower bounds for the free energies are independent of $\phi$, given by:

$$\begin{array}{lcccr}
\displaystyle {f_{\mit hex}\over f_{\mit cyl}} 
&=& {\displaystyle\left({10\over 9}\right)^{1/3}} &\simeq& 1.036 \\
\noalign{\vskip10truept}
\displaystyle {f_{\mit square}\over f_{\mit cyl}} 
&=& {\displaystyle\left({4\over 3}\right)^{1/3}}&\simeq& 1.101 \\
\noalign{\vskip10truept}
\displaystyle {f_{\mit bcc}\over f_{\mit sph}} 
&=& {\displaystyle\left(95\over 384\right)^{1/3}\left({1\over 2}
+\sqrt{3}\right)^{2/3}} &\simeq& 1.072 \\
\noalign{\vskip10truept}
\displaystyle {f_{\mit fcc}\over f_{\mit sph}} 
&=& {\displaystyle\left({5\over 4}\right)^{1/3}} &\simeq& 1.077.
\end{array}$$

Evidently, the most favorable structures have the “roundest” unit cells. The hexagonal phase is favored over the square phase, and BCC is 