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, ${\mathrm{U}}_f(7)$ and ${\mathrm{SO}}_{sf}(8)$. 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.

在具有s和f玻色子的相互作用玻色子模型sf -IBM的情况下，推导了旋转不变且具有奇偶性的哈密顿量（最多具有两体相互作用）的条件，该条件在其经典极限中具有四面体形状的最小值。可以在模型的两个极限之间过渡的哈密顿量的经典极限中获得包括具有四面体对称形状的简并极小值，${\mathrm{ü}}_F（7）$ 和 ${\mathrm{所以}}_{sF}（8）$。得出存在这样的最小值的条件。该系统可以通过朝向的之间的两个体相互作用的修饰的分离的最小与四面体形状来驱动˚F玻色子。对于代数模型中具有较高秩离散对称的形状的观测结果，提出了一般性评论。