  The starting point is the problem of finding the interaction energy of two
coinciding homogeneous cubic charge distributions. The brute force method of
subdividing the cube into $N^3$ sub-cubes and doing the sums results in slow
convergence because of the Coulomb singularity. Using symmetry and algebra the
Coulomb singularities can be eliminated. This leads to an accurate numerical
algorithm as well as an interesting exact result relating the desired
interaction energy to three other interaction energies, namely those of cubes
touching each other at a face, at an edge, and at a corner, respectively. As an
application a simple model illustrating Wigner crystallization is presented.
