  Matrices of the irreducible representations of double crystallographic point
groups O, Td, Ox{1,I} and Tdx{1,I} are derived. The characteristic polynomials
(spinor bases) up to the sixth power are obtained. The method for the
derivation of the general form of an arbitrary matrix element of a
vector/tensor quantity is developed; as an application, the kp matrix elements
are calculated. It is demonstrated that the other known method for obtaining
the bases of the irreducible representations of the double groups
(LS-diagonalization of a linear combination of spherical harmonics) is
unreliable.
