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We show that any SU (2) BPS monopole of charge k with rotational spatial dihedral symmetry is gauge equivalent to the Nahm data obtained from affine Toda equations of Cₗ^ (1) type when k=2l or A₂ (₋-₁) ^ (2) type when k=2l-1.
Braden et al. (Tue,) studied this question.