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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.
For example, in the rock salt ionic structure each sodium atom has six near neighbour chloride ions in an octahedral geometry and each chloride has similarly six near neighbour sodium ions in an octahedral geometry. In metals with the body centred cubic (bcc) structure each atom has eight nearest neighbours in a cubic geometry.
The two octahedral cells project onto the entire volume of this envelope, while the 8 triangular prismic cells project onto its 8 triangular faces. The triangular-prism-first orthographic projection of the octahedral prism into 3D space has a hexagonal prismic envelope. The two octahedral cells project onto the two hexagonal faces.
Octahedral (red) and tetrahedral (blue) interstitial sites in a face-centered cubic lattice. Interstitial sites refer to the empty spaces in between the atoms in the crystal lattice. These spaces can be filled by oppositely charged ions to form multi-element structures.
Examples of the capped octahedral molecular geometry are the heptafluoromolybdate (MoF − 7) and the heptafluorotungstate (WF − 7) ions. [3] [4] The "distorted octahedral geometry" exhibited by some AX 6 E 1 molecules such as xenon hexafluoride (XeF 6) is a variant of this geometry, with the lone pair occupying the "cap" position.
An octahedral void could fit an atom with a radius 0.414 times the size of the atoms making up the lattice. [1] An atom that fills this empty space could be larger than this ideal radius ratio, which would lead to a distorted lattice due to pushing out the surrounding atoms, but it cannot be smaller than this ratio.
One example of the bicapped trigonal prismatic molecular geometry is the ZrF 4− 8 ion. [1] The bicapped trigonal prismatic coordination geometry is found in the plutonium(III) bromide crystal structure type, which is adopted by many of the bromides and iodides of the lanthanides and actinides. [2] [3]
A high-index reflective subgroup is the prismatic octahedral symmetry, [4,3,2] (), order 96, subgroup index 4, (Du Val #44 (O/C 2;O/C 2) *, Conway ± 1 / 24 [O×O].2). The truncated cubic prism has this symmetry with Coxeter diagram and the cubic prism is a lower symmetry construction of the tesseract, as .