  Octupolar tensors are third order, completely symmetric and traceless
tensors. Whereas in 2D an octupolar tensor has the same symmetries as an
equilateral triangle and can ultimately be identified with a vector in the
plane, the symmetries that it enjoys in 3D are quite different, and only
exceptionally reduce to those of a regular tetrahedron. By use of the octupolar
potential that is, the cubic form associated on the unit sphere with an
octupolar tensor, we shall classify all inequivalent octupolar symmetries. This
is a mathematical study which also reviews and incorporates some previous, less
systematic attempts.
