Symmetrical properties of soccerane and its derivatives are discussed in the light of subduction of coset representations (CRs). The 60 vertices of soccerane are equivalent and construct a single orbit governed by the CR, Ih(/Cs). This orbit is divided into several orbits in the respective derivative, where the mode of the division is controlled by the subduction. The number of derivatives with a given formula and a given subsymmetry is calculated in terms of unit subduced cycle indices, which are derived from the subduction.
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Shinsaku Fujita (1991) studied this question.
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