  Projective symmetry groups are applied to Raman observations of the Kitaev
quantum spin liquids in spherical lattice geometries realized by Platonic and
Archimedean polyhedra. Parton single excitations in Kitaev spin polyhedra are
characterized by double-valued irreducible representations of their belonging
projective symmetry groups, whereas parton geminate excitations relevant to
Raman scattering are decomposed into single-valued irreducible representations
of the corresponding point symmetry groups. We combine a standard
point-symmetry-group analysis of the Loudon-Fleury vertices and an elaborate
projective-symmetry-group analysis of itinerant spinons against the ground
gauge fields to reveal $hidden$ $selection$ $rules$ for Raman scattering in
$\mathbb{Z}_2$ spin liquids.
