  We find a solution to Einstein field equations for a regular toroidal lattice
of size L with equal masses M at the centre of each cell; this solution is
exact at order M/L. Such a solution is convenient to study the dynamics of an
assembly of galaxy-like objects. We find that the solution is expanding (or
contracting) in exactly the same way as the solution of a
Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average
density as our model. This points towards the absence of backreaction in a
Universe filled with an infinite number of objects, and this validates the
fluid approximation, as far as dynamics is concerned, and at the level of
approximation considered in this work.
