Fig. 5.

Space-filling representations of the crystal structures for the BCC ($Im\overline{3}m$ space group) and Frank–Kasper σ ($P{4}_2\text{/}mnm$) phases. The faceted polyhedrons represent self-assembled particles that must fill space at uniform density, necessitating distortions in size and shape imposed by the lattice symmetry. The BCC crystal contains one particle per lattice site, each formed from ∼193 block copolymer molecules. The σ-phase has 30 particles per lattice site, split among 5 discrete polyhedral with varying size and shape, at the indicated Wyckoff positions (2b, 4f, 8i, 8i′, 8j, where occupancy is denoted by the integer). The relative volume of each polyhedral is satisfied by varying the number of molecules per particle between approximately 176 and 206.