The symmetries of the sdg-IBM, the interacting boson model with s, d and g bosons, are studied as regards the occurrence of shapes with octahedral symmetry. It is shown that no sdg-IBM Hamiltonian with a dynamical symmetry displays in its classical limit an isolated minimum with octahedral shape. However, a degenerate minimum that includes a shape with octahedral symmetry can be obtained from a Hamiltonian that is transitional between two limits, ${\mathrm{U}}_g(9)\otimes {\mathrm{U}}_d(5)$ and ${\mathrm{SO}}_{sg}(10)\otimes {\mathrm{U}}_d(5)$, and the conditions for its existence are derived. An isolated minimum with octahedral shape, either an octahedron or a cube, may arise through a modification of two-body interactions between the g bosons. Comments on the observational consequences of this construction are made.

研究了sdg -IBM的对称性（具有s，d和g玻色子的相互作用玻色子模型）关于八面体对称形状的出现。结果表明，没有具有动力学对称性的sdg -IBM Hamiltonian在其经典极限中显示出具有八面体形状的孤立最小值。但是，可以从在两个极限之间过渡的哈密顿量获得包括八面体对称形状的简并极小值，${\mathrm{ü}}_G（9）\otimes {\mathrm{ü}}_d（5）$ 和 ${\mathrm{所以}}_{sG}（10）\otimes {\mathrm{ü}}_d（5）$，并推导出其存在的条件。通过改变g玻色子之间的两体相互作用，可以产生具有八面体形状（八面体或立方体）的孤立最小值。对这种构造的观测结果进行了评论。