  In the context of the sf-IBM, the interacting boson model with s and f
bosons, the conditions are derived for a rotationally invariant and
parity-conserving Hamiltonian with up to two-body interactions to have a
minimum with tetrahedral shape in its classical limit. A degenerate minimum
that includes a shape with tetrahedral symmetry can be obtained in the
classical limit of a Hamiltonian that is transitional between the two limits of
the model, U_f(7) and SO_{sf}(8). The conditions for the existence of such a
minimum are derived. The system can be driven towards an isolated minimum with
tetrahedral shape through a modification of two-body interactions between the f
bosons. General comments are made on the observational consequences of the
occurrence of shapes with a higher-rank discrete symmetry in the context of
algebraic models.
