  This paper examines the properties of `lattice universes' wherein point
masses are arranged in a regular lattice on space-like hypersurfaces; open,
flat, and closed universes are considered. The universes are modelled using the
Lindquist-Wheeler (LW) approximation scheme, which approximates the space-time
in each lattice cell by Schwarz\-schild geometry. Extending Lindquist and
Wheeler's work, we derive cosmological scale factors describing the evolution
of all three types of universes, and we use these scale factors to show that
the universes' dynamics strongly resemble those of
Friedmann-Lema\^itre-Robertson-Walker (FLRW) universes. In particular, we use
the scale factors to make more salient the resemblance between Clifton and
Ferreira's Friedmann-like equations for the LW models and the actual Friedmann
equations of FLRW space-times. Cosmological redshifts for such universes are
then determined numerically, using a modification of Clifton and Ferreira's
approach; the redshifts are found to closely resemble their FLRW counterparts,
though with certain differences attributable to the `lumpiness' in the
underlying matter content. Most notably, the LW redshifts can differ from their
FLRW counterparts by as much as 30\%, even though they increase linearly with
FLRW redshifts, and they exhibit a non-zero integrated Sachs-Wolfe effect,
something which would not be possible in matter-dominated FLRW universes
without a cosmological constant.
