  The geometrical construction of rational maps using a cubic grid has led to
many new Skyrmion solutions, with baryon numbers up to 108. Energy spectra of
some of the new Skyrmions are calculated here by semi-classical quantization.
Quantization of the B=20 T_d-symmetric Skyrmion, which is one of the newly
found Skyrmions, is considered, and this leads to the development of a new
approach to solving Finkelstein-Rubinstein (F-R) constraints. Matrix equations
are simplified by introducing a Cartesian version of angular momentum basis
states, and the computations are easier. The quantum states of all
T_d-symmetric Skyrmions, constructed from the cubic grid, are classified into
three classes, depending on the contribution of vertex points of the cubic grid
to the rational maps. The analysis is extended to the larger symmetry group
O_h. Quantum states of O_h-symmetric Skyrmions, constructed from the cubic
grid, form a subset of the T_d-symmetric quantum states.
