  Applications to holographic theories have led to some recent interest in
magnetic monopoles in four-dimensional Anti-de Sitter spacetime. This paper is
concerned with a study of these monopoles, using both analytic and numerical
methods. An approximation is introduced in which the fields of a charge N
monopole are explicitly given in terms of a degree N rational map. Within this
approximation, it is shown that the minimal energy monopole of charge N has the
same symmetry as the minimal energy Skyrmion with baryon number N in Minkowski
spacetime. Beyond charge two the minimal energy monopole has only a discrete
symmetry, which is often Platonic. The rational map approximation provides an
upper bound on the monopole energy and may be viewed as a smooth non-abelian
refinement of the magnetic bag approximation, to which it reverts under some
additional approximations. The analytic results are supported by numerical
solutions obtained from simulations of the non-abelian field theory. A similar
analysis is performed on the monopole wall that emerges in the large N limit,
to reveal a hexagonal lattice as the minimal energy architecture.
