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full octahedral symmetry: This group has the same rotation axes as O, but with mirror planes, comprising both the mirror planes of T d and T h. The three-fold axes give rise to four D 3d subgroups. The three perpendicular four-fold axes of O now give D 4h subgroups, while the six two-fold axes give six D 2h subgroups.
The term "octahedral" is used somewhat loosely by chemists, focusing on the geometry of the bonds to the central atom and not considering differences among the ligands themselves. For example, [Co(NH 3 ) 6 ] 3+ , which is not octahedral in the mathematical sense due to the orientation of the N−H bonds, is referred to as octahedral.
Natural crystals of diamond, alum or fluorite are commonly octahedral, as the space-filling tetrahedral-octahedral honeycomb. The plates of kamacite alloy in octahedrite meteorites are arranged paralleling the eight faces of an octahedron. Many metal ions coordinate six ligands in an octahedral or distorted octahedral configuration.
3D model of a truncated octahedron. The truncated octahedron is one of the thirteen Archimedean solids. In other words, it has a highly symmetric and semi-regular polyhedron with two or more different regular polygonal faces that meet in a vertex. [3] The dual polyhedron of a truncated octahedron is the tetrakis hexahedron.
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O h, *432, [4,3], or m3m of order 48 – achiral octahedral symmetry or full octahedral symmetry. This group has the same rotation axes as O, but with mirror planes, comprising both the mirror planes of T d and T h. This group is isomorphic to S 4.C 2, and is the full symmetry group of the cube and octahedron. It is the hyperoctahedral group ...