Y_4^0 + \sqrt{5}\:Y_4^4 + {\rm c.c.} \label{eq:cube}\\
&D_4 && \ell=5&& \zeta - {R}\propto \sqrt{3}\: Y_5^0 + \sqrt{5} \: Y_5^4 + {\rm c.c.}\label{eq:D4}\\
&\mbox{Icosahedral} && \ell=6 &&\zeta - {R}\propto \sqrt{11} \: Y_6^0  + \sqrt{14} \: Y_6^5 + {\rm c.c.} \label{eq:icosa}\end{aligned}$$

\[eq:formulas\]

  -------- ------------- --------- ------------------- ----------- --------- -------------- -------------------
           Temporal                                                Initial   Final          
  $\ell$   Response                          Amplitude   Frequency           Condition      Pattern
                         $a/a_g$     $\omega/\omega_g$                                      
  1        harmonic                               0.30        1.00           spherical      translational
  2        harmonic                               0.50        1.37           axisymmetric   prolate-oblate
                         $a/a_c$     $\omega/\omega_c$                                      
  3        subharmonic                           13.53       13.21           axisymmetric   tetrahedral
  4        subharmonic                            5.07       16.61           axisymmetric   axisymmetric
  4        subharmonic                            5.07       16.61           cubic          cubic-octahedral
  5        subharmonic                           22.00       25.02           axisymmetric   $D_4$
  6        subharmonic                           16.07       30.63           icosahedral    no stable pattern
  -------- ------------- --------- ------------------- ----------- --------- -------------- -------------------

  : Parameters of imposed forcing and of the observed response.[]{data-label="tab:forcing_response"}

![Instability tongues resulting from oscillatory forcing with amplitude $a$ and angular frequency $\omega$ for an inviscid drop with parameters given in table \[tab:forcing\_response\]. Diamond shapes designate the parameter values of our simulations. Solid curves bound subharmonic tongues and dashed curves bound harmonic tongues. (a) Tongues corresponding to gravitational instability with spherical wavenumbers $\ell=1$, 2, 3, 4 originate at $\omega/\omega_g =
  2\sqrt{\ell}/n$, with $n=1$ for subharmonic tongues and $n=2$ for harmonic tongues. (b) Tongues corresponding to capillary instability 