= Solution
For ideal spherical <micelles>, $v/a_0=r/3$ and $r\leq\ell_c$, giving $P\leq1/3$. For a long cylindrical <micelle>, $v/a_0=r/2$, so cylinders can accommodate larger packing parameters while keeping $r\leq\ell_c$: \b[roughly $1/3<P\lesssim1/2$ favours cylinders]. Relatively small head area or greater tail volume reduces positive curvature.
For a planar bilayer leaflet of hydrophobic thickness $\ell$, $v/a_0\simeq\ell$, with $\ell\leq\ell_c$. Thus \b[$1/2\lesssim P\lesssim1$ favours bilayer/vesicle structures], with nearly planar bilayers toward $P\simeq1$. The two leaflets put hydrophobic tails together and hydrophilic heads toward water. For $P>1$, inverse structures become possible. These bounds are approximate packing guides; chain stretching, head interactions and aggregate <free energy> determine actual phase boundaries.
<Theory of self-assembly of hydrocarbon amphiphiles by Jacob N. Israelachvili and others>[General <micelle>/bilayer geometrical packing model]{ref}
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