  Why are materials with specific characteristics more abundant than others?
This is a fundamental question in materials science and one that is
traditionally difficult to tackle, given the vastness of compositional and
configurational space. We highlight here the anomalous abundance of inorganic
compounds whose primitive unit cell contains a number of atoms that is a
multiple of four. This occurrence - named here the 'rule of four' - has to our
knowledge not previously been reported or studied. Here, we first highlight the
rule's existence, especially notable when restricting oneself to experimentally
known compounds, and explore its possible relationship with established
descriptors of crystal structures, from symmetries to energies. We then
investigate this relative abundance by looking at structural descriptors, both
of global (packing configurations) and local (the smooth overlap of atomic
positions) nature. Contrary to intuition, the overabundance does not correlate
with low-energy or high-symmetry structures; in fact, structures which obey the
'rule of four' are characterized by low symmetries and loosely packed
arrangements maximizing the free volume. We are able to correlate this
abundance with local structural symmetries, and visualize the results using a
hybrid supervised-unsupervised machine learning method.
