Packing fraction of a disk assembly randomly close packed on a plane

A simple model is used to show that, in principle, random close packing of equal disks on a plane should be stable when the packing fraction is 0.813, the average number of contacts per disk is 3.42, and the connectivity of the simplicial net is 4. The assembly is unstable with respect to shear stresses, which will be a consequence of compressive stresses applied to the randomly packed assembly. In practice, the packing fraction of the assembly will increase until it reaches the value associated with the triangulated simplicial net, the regularly packed disk assembly.