leads to a qualitatively different situation. We will explore the motion and shape of an oscillating drop for values of $\ell$ up to 6.

Methods
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Pattern formation on a sphere
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Our previous paper [@Ali1] concerns the linear stability, via Floquet analysis, of the spherical Faraday problem. As is the case for all spherically symmetric problems, the equation governing the linear stability does not depend on the order $m$ of the spherical harmonic. Therefore, a bifurcation from the spherically symmetric state involves $2\ell+1$ linearly independent solutions ($Y_\ell^m$ with $ -\ell \leq
m \leq \ell$) with the same growth rate. The combination of these modes, i.e. the pattern, that can result from such a bifurcation is determined by the nonlinear terms. A pattern with a given $\ell$ cannot be associated with a unique combination of modes $m$, since rotation of a spherical harmonic changes $m$ (but not $\ell$).

Symmetry groups provide a classification of patterns which does not depend on orientation. A number of researchers [@Busse1975; @BR1982; @Riahi1984; @IG1984; @Golubitsky; @Chossat1991; @Matth2003] have studied the patterns which are allowed and those which are preferred for various values of $\ell$. Patterns that appear at bifurcations can be associated with a subgroup 