The best understood crystal ordering transition is that of two-dimensional freezing, which proceeds by the rapid eradication of lattice defects as the temperature is lowered below a critical threshold(1-4). But crystals that assemble on closed surfaces are required by topology to have a minimum number of lattice defects, called disclinations, that act as conserved topological charges-consider the 12 pentagons on a football or the 12 pentamers on a viral capsid(5,6). Moreover, crystals assembled on curved surfaces can spontaneously develop additional lattice defects to alleviate the stress imposed by the curvature(6-8). It is therefore unclear how crystallization can proceed on a sphere, the simplest curved surface on which it is impossible to eliminate such defects. Here we show that freezing on the surface of a sphere proceeds by the formation of a single, encompassing crystalline `continent', which forces defects into 12 isolated `seas' with the same icosahedral symmetry as footballs and viruses. We use this broken symmetry-aligning the vertices of an icosahedron with the defect seas and unfolding the faces onto a plane-to construct a new order parameter that reveals the underlying long-range orientational order of the lattice. The effects of geometry on crystallization could be taken into account in the design of nanometre-and micrometre-scale structures in which mobile defects are sequestered into self-ordered arrays. Our results may also be relevant in understanding the properties and occurrence of natural icosahedral structures such as viruses(5,9,10).