  It is known that any tame hyperbolic 3-manifold with infinite volume and a
single end is the geometric limit of a sequence of finite volume hyperbolic
knot complements. Purcell and Souto showed that if the original manifold embeds
in the 3-sphere, then such knots can be taken to lie in the 3-sphere. However,
their proof was nonconstructive; no examples were produced. In this paper, we
give a constructive proof in the geometrically finite case. That is, given a
geometrically finite, tame hyperbolic 3-manifold with one end, we build an
explicit family of knots whose complements converge to it geometrically. Our
knots lie in the (topological) double of the original manifold. The
construction generalises the class of fully augmented links to a Kleinian
groups setting.
