A reduction of orbits of finite reflection groups to their reflection subgroups is produced by means of projection matrices, which transform points of the orbit of any group into points of the orbits of its subgroup. Projection matrices and branching rules for orbits of finite Coxeter groups of non-crystallographic type are presented. The novelty in this paper is producing the branching rules that involve non-crystallographic Coxeter groups. Moreover, these branching rules are relevant to any application of non-crystallographic Coxeter groups including molecular crystallography and encryption.
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