The problem of three-dimensional convection in spherical shells is considered in the case of spherically symmetric physical conditions for a Boussinesq fluid. While the question of the preferred patterns of convection has been treated in earlier papers, general rules for the flow direction have not yet been found. The present analysis addresses this problem and presents numerical solutions for convection in a fluid of infinite Prandtl number with octohedral or with dodecahedral symmetry as a function of the Rayleigh number.