  Certain hyperbolic monopoles and all hyperbolic vortices can be constructed
from SO(2) and SO(3) invariant Euclidean instantons, respectively. This
observation allows us to describe a large class of hyperbolic monopoles as
hyperbolic vortices embedded into $\mathbb{H}^3$ and yields a remarkably simple
relation between the two Higgs fields. This correspondence between vortices and
monopoles gives new insight into the geometry of the spectral curve and the
moduli space of hyperbolic monopoles. It also allows an explicit construction
of the fields of a hyperbolic monopole invariant under a $\mathbb{Z}$ action,
which we compare to periodic monopoles in Euclidean space.
