  We present a generalized Landau-Brazovskii theory for the solidification of
chiral molecules on a spherical surface. With increasing sphere radius one
encounters first intervals where robust achiral density modulations appear with
icosahedral symmetry via first-order transitions. Next, one en- counters
intervals where fragile but stable icosahedral structures still can be
constructed but only by superposition of multiple irreducible representations.
Chiral icoshedral structures appear via continuous or very weakly first-order
transitions. Outside these parameter intervals, icosahedral symmetry is broken
along a three-fold axis or a five-fold axis. The predictions of the theory are
compared with recent numerical simulations.
