In this thesis, we have constructed new analytical solutions for initial data of the Einstein equations. Such solutions are valuable for gaining a better understanding of problems involving strong gravitational and/or electromagnetic interactions in general relativity. In this process we have examined an inhomogeneous cosmological model consisting a lattice of regularly arranged, charged black holes with initial data corresponding to the maximum expansion of a cosmological solution. We have also refined the method in such a way that the values of the mass and charge of the sources can be prescribed beforehand subject to certain constraints dictated by the field equations. Then we studied a two dimensional ‘equatorial’ cross-section of the initial data space and presented the behaviour of the local curvature for the slices of the Platonic bodies 8, 16, 24, 120 and compared black hole lattices with a Friedmann universe of a unit radius. We see that the black hole lattice is not close to this, or any other, round sphere as far as its local curvature is concerned. For all Platonic solutions, the black hole regions are located where the curvature assumes its minimum value, and it strikes the eye that they are well isolated from each other and do not distort each other noticeably. On the other hand, we confirm that black holes themselves are remarkably round in the strong curvature regions. The recent surge of interest in these solutions was driven by the cosmological averaging problem. Is it likely to affect our understanding of the dark side of the universe in a significant way? We feel that the right way to go may well be to find other interesting toy models, where agreement can be reached quickly.