The Archimedean truncated octahedron. II. Crystal structures with geometric units of symmetry 43m

Abstract

All geometric units in crystal structures of space groups P{\bar 4}3m, I{\bar 4}3m, Pn3m, F{\bar 4}3m and Fd3m possess point group {\bar 4}3m. These units may be vacant, or may contain one or more atoms. In units containing more atoms than one, the atoms form one or a collection of these polyhedra: tetrahedron, truncated tetrahedron, octahedron, cuboctahedron or truncated octahedron; the last two may be distorted. Therefore, a formula that lists the consecutive polyhedra starting from the center of the unit can be used for the tabulation of these crystal structures. Only structures of Cu2O type are known in Pn3m and typical structures of the other four space groups are tabulated.