Searching for the perfect packing

Extremely dense granular packings are needed for high resistance concrete or hard ceramics. They can only be realised when the size distribution of grains is strongly polydisperse. Typically power law distributions give the best results. We present a simple packing model for polydisperse distributions, namely a generalized reversible parking lot model. We also discuss the perfect limit of Apollonian packings in three dimensions and show in particular the existence of space filling bearings rotating without slip and without torsion.