@article {15327,
	title = {The Archimedean truncated octahedron. III. Crystal structures with geometric units of symmetry m3m},
	journal = {Acta Cryst. (1982). A38, 346-349},
	year = {1982},
	abstract = {All geometric units in crystal structures of space groups\&nbsp;Im3m\&nbsp;and\&nbsp;Pm3m\&nbsp;and two out of the three types in those of\&nbsp;Fm3m\&nbsp;have\&nbsp;m3m\&nbsp;symmetry, whereas the remaining one of\&nbsp;Fm3m\&nbsp;possesses\&nbsp;3m\&nbsp;symmetry. Theoretically, a geometric unit of\&nbsp;m3m\&nbsp;symmetry has atoms arranged as a collection of these possible polyhedra: octahedron, cube, cuboctahedron, truncated octahedron, truncated cube, small rhombicuboctahedron and rhombicuboctahedron. All these can be derived from truncations, sometimes repeated, of the pair of platonic solids, cube and octahedron, which possess\&nbsp;m3m\&nbsp;symmetry. In reality, no known crystal structure has a geometric unit with a rhombicuboctahedron or a truncated cube. The close-packing requirement causes a complicated geometric unit to start (from the center) in one of the following ways: (i) a single atom followed by an octahedron, (ii) a single atom followed by a cube, (iii) an octahedron and (iv) a cube. The survey of structures indicates that polyhedra derived from an octahedron occur more frequently in real geometric units than those related to a cube.},
	url = {https://doi.org/10.1107/S0567739482000722},
	author = {Chung Chieh}
}
