  In this paper, we present the implicit equations for one special class of
real-valued spherical harmonics with octahedral symmetry. Based on this
representation, we construct the rotationally invariant measure of deviation
from the specified symmetry. The spherical harmonics we consider have some
applications in the area of directional fields design due to their ability to
represent mutually orthogonal axes in 3D space, not relative to their order and
orientation.
