Dihedrally symmetric monopoles and affine Toda equations

Abstract

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 $C_l^{(1)}$ type when $k=2l$ or $A_{2(l-1)}^{(2)}$ type when
$k=2l-1$.