Table 2.

Locations of centers $q_z^{mn}$ divided by 2π/a where a is the long lattice constant and $b=a∕\sqrt{3}$. Flat gel is indicated by L and ripple by P and β indicates tilt by angle θ relative to the bilayer normal. The major arm angle ξ and the orientation ζ of the unit cell are defined in Fig. 5 where the angle ϕ = 0 gives the F phase and ϕ = π/2 gives the I phase.

	(±2,0)	(±1,1)	(±1,−1)
LβI	0	$\sqrt{3}\sin \theta$	$-\sqrt{3}\sin \theta$
$P_{\beta I}^{\zeta =0}$	0	$\sqrt{3}\sin (\theta -\xi )$	$-\sqrt{3}\sin (\theta -\xi )$
$P_{\beta I}^{\zeta =\pi ∕2}$	±2sinξ	$\sqrt{3}\sin \theta \cos \xi \pm \sin \xi$	$-\sqrt{3}\sin \theta \cos \xi \pm \sin \xi$
	(±2,0)	(1,±1)	(−1,±1)
LβF	±2tanθ	tanθ	−tanθ
$P_{\beta F}^{\zeta =0}$	$\pm 2\tan \theta \cos \xi$	$\tan \theta \cos \xi \mp \sqrt{3}\sin \xi ∕\cos \theta$	$-(\tan \theta \cos \xi \mp \sqrt{3}\sin \xi ∕\cos \theta )$
$P_{\beta F}^{\zeta =\pi ∕2}$	$\pm 2(\tan \theta \cos \xi +\sin \xi )$	$\tan \theta \cos \xi +\sin \xi$	$-(\tan \theta \cos \xi +\sin \xi )$