of identifying transition points between different phases, a fact that can unequivocally define RCP as the freezing point in a discontinuous transition. This formalism may be useful in analyzing other related transitions in complex systems ranging from optimization problems in computer science [29] to the physics of glasses [6]. Other unsolved packing problems in- cluding finding the densest arrangement of rods, ellipsoids, spherocylinders, binary mixtures, Platonic and Archimedean solids—which are known to pack better than spheres [9, 30]—can now be analyzed from the proposed thermodynamic view of phase transitions. 

