  Spherical harmonics of degree 4 are widely used in volumetric frame fields
design due to their ability to reproduce octahedral symmetry. In this paper we
show how to use harmonics of degree 3 (octupoles) for the same purpose, thereby
reducing number of parameters and computational complexity. The key ingredients
of the presented approach are
  \quad \textbullet \ implicit equations for the manifold of octupoles
possessing octahedral symmetry up to multiplication by $-1$,
  \quad \textbullet \ corresponding rotationally invariant measure of
octupole's deviation from the specified symmetry,
  \quad \textbullet \ smoothing penalty term compensating the lack of
octupoles' symmetries during a field optimization.
