  We argue that 2D dodecagonal spherical quasicrystalls (QCs) will be
discovered in the nearest future and investigate how the planar QC order
becomes compatible with the spherical geometry. We show that the appearance of
curvature-induced topological defects and low-energy structural rearrangements
are sufficient to obtain the regular spherical QC structures. Minimization of
total energy required for the order reconstruction determines the number of
topological defects, which are located near the vertices of snub cub or
icosahedron in dependence on type of the initial dodecagonal order.
