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

Landau Theory and the Emergence of Chirality in Viral Capsids