Hard colloidal spheres present a certain degree of local ordering that has been in the past described in different (related) ways: one can identify an increased role played by tetrahedral arrangements, or focus on icosahedral or partially icosahedral structures.
Expanding on a previous work, James Hallett (now in Oxford) has produced earlier this year a detailed analysis of very high density experiments where we show that increased local ordering can be described in terms of the number of interlacing pentagonal rings formed by neighbouring particles. This provides a finer description of the changes that high densities impose on the local structure and on the geometric constraints that are satisfied (or not) by the microscopic reordering.
The full work is available on the Journal of Statistical Mechanics.
James E Hallett, Francesco Turci, C. Patrick Royall J. Stat. Mech.014001 (2020)