The cube and the natural geometry of fragmentation

Abstract:

If we approximate natural fragments by convex polyhedra and count the respective numbers for faces,
vertices and edges then in most cases we find averages close to 6,8,12,
the values corresponding to the cube. By vetting field data from over 4000 natural fragments against
computer simulations we showed [1] that hyperplane mosaics as mathematical models can not only
capture this interesting natural phenomenon, but also reproduce distributions
for many geophysical shape decsriptors with remarkable accuracy.

We also found that stress fields determine fragmentation patterns
(albeit in an averaged sense) and the vast majority of naturally
occurring stress fields produce patterns which yield fragments with cuboid averages.