  In this paper we propose to use Lie sphere-geometry as a new tool to
systematically construct time-symmetric initial data for a wide variety of
generalised black-hole configurations in lattice cosmology. These
configurations are iteratively constructed analytically and may have any degree
of geometric irregularity. We show that for negligible amounts of dust these
solutions are similar (in a sense made precise) to the swiss-cheese models at
the moment of maximal expansion. As Lie sphere-geometry has so far not received
much attention in cosmology, we will devote a large part of this paper to
explain its geometric background in a language familiar to general relativists.
