Fig. 2
From: Revealing and exploiting hierarchical material structure through complex atomic networks
The structure of α-B12 (in the 36 atom hexagonal unit cell) and its modular decompositions. As established by the modularity decomposition the simplest way of describing this structure is as three interconnected icosahedra. For the purpose of comparison we also show an alternative, less efficient decomposition into six units of six atoms with C3v symmetry. These units correspond to halves of the icosahedra. The decomposition that minimises the amount of information I (normalised here by the maximum value of 3N − 6) required to describe the crystal structure, occurs for values around w s = 1 (modularity tuning parameter) and d * = 2.5 Å (interatomic distance threshold). This decomposition occupies a broad plateau (darkest shade of green) in the 2D space of the modularity tuning parameter w s and the interatomic distance threshold d *
