  Let M be a complete hyperbolic 3-manifold of finite volume that admits a
decomposition into right-angled ideal polyhedra. We show that M has a
deformation retraction that is a virtually special square complex, in the sense
of Haglund and Wise and deduce that such manifolds are virtually fibered. We
generalise a theorem of Haglund and Wise to the relatively hyperbolic setting
and deduce that the fundamental group of M is LERF and that the geometrically
finite subgroups of the fundamental group are virtual retracts. Examples of
3-manifolds admitting such a decomposition include augmented link complements.
We classify the low-complexity augmented links and describe an infinite family
with complements not commensurable to any 3-dimensional reflection orbifold.
