  We solve "half" the problem of finding three-dimensional quasisymmetric
magnetic fields that do not necessarily satisfy force balance. This involves
determining which hidden symmetries are admissible as quasisymmetries, and then
showing explicitly how to construct quasisymmetric magnetic fields given an
admissible symmetry. The admissibility conditions take the form of a system of
overdetermined nonlinear partial differential equations involving second
derivatives of the symmetry's infinitesimal generator.
