An exact appolonian packing is generated in two, three, and four dimensions using Soddy's formula. The fractal dimension is determined in each case and agrees with values found in the literature for two- and three-dimensional appolonian packings generated by other techniques. It is shown that the sphere size distribution cannot in practice lead to the fractal dimension of the appolonian packing for d > 2. The origin of this effect is the non-power law, bell-shaped size distribution, as observed in natural systems like stones and sediments, naturally generated by Soddy's formula for a finite number of iterations.