Acad Sinica, Inst High Energy Phys, Beijing 100039, Peoples R China
; Kansas State Univ, Dept Phys, Manhattan, KS 66506 USA
; Univ Three Gorges, Dept Phys, Yichang 443000, Peoples R China
; Natl Autonomous Univ Mexico, Inst Ciencias Nucl, Mexico City 04510, DF, Mexico
The irreducible bases of the icosahedral double groups I' acid I-h' are explicitly presented in their respective group spaces. Applying these bases to the spin states \j, mu >, we obtain a simple formula for combining the spin states into the symmetry-adapted bases which belong to a given row of given irreducible representations of I' and I-h'.