In each case a generic point in V identifies it with the complexification of a Jordan algebra of 3 x 3 hermitian matrices (over the division algebras R, C, H and O respectively) and the cubic relative invariant is identified with a suitable determinant. The isotropy algebra of such a generic point, the Lie algebra of G and the Lie algebra of H give the complexifications of the first three rows of the Freudenthal magic square.
