We study the ground state properties of the discrete spin cubic model
situated on the Sierpinski gasket fractal lattice. The relevant model
Hamiltonian contains exchange and quadrupolar interaction terms, assoc
iated with the parameters J(1) and J(2), respectively. We have found t
hat the model under study has a very rich ground state diagram in the
(J(1),J(2))-plane, with one ordered (ferromagnetic) state and three re
gions of different frustrated states.