Octahedra sharing only edges

Crystalline TCCI4 provides a simple example of the skew chain, which is also found as the form of the aquo-anion in the dihydrate of UCUCI3. One-half of the molecules of water of crystallization are incorporated into the chain and the remainder, together with the Li ions, are accommodated between the chains. Other examples include the anion in (CsH5NH)(SbCl4) and the chain molecules 174 

Octahedra sharing (a) skew edges and (b) trans edges. 

There is also a family of structures containing rutile-like chains which are held 

Projection of the structure of Na2MnCl4 along the direction of the chain ions. 

Structures formed from octahedra sharing 2, 4 or 6 edges.  

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Between adjacent layers in hexagonal eutaxy both octahedra and tetrahedra share faces (with their own kind) whereas in cubic eutaxy tetrahedra share faces only with octahedra, and vice versa. The latter situation also obtains within layers (in both kinds of eutaxy) then octahedra share only edges with other octahedra, and similarly tetrahedra share only edges with each other... 

Each octahedron shares six edges with dodecahedra and only corners with tetrahedra. Each tetrahedron shares two edges with dodecahedra octahedra and dodecahedra share only corners. Each dodecahedron... 

Liger et al. (1999) suggested another explanation that, in fact, better explains the pattern of their results. Whereas sorbed uranyl commonly shares an edge of its polyhedron with the hematite octahedron, they proposed that some of the uranyl shares only an apex. If the apical site were not catalytic, reaction would slow as the uranyl was depleted at the normal, but not the apical sites. For such a scenario to explain the data, the site would need to be less abundant than the normal sites, but sorb uranyl more strongly. 

Only the second one is possible and we should have n — p. If j = 3, then G is Octahedron. At every vertex of Octahedron, we have two ways to put 2-gons. Those possibilities are indexed by a pair of 3-gons sharing only an edge. Since we have 6 vertices, this makes 64 possibilities and, up to isomorphism, 7 possibilities. Clearly, every 3-gon should belong to at least one pair. This restricts us to three possibilities. The first possibility is shown below with the number associated to each vertex ... 

The isolated Mo06 octahedron is known only in condensed units, where the Mo06 polyhedra share corners, edges and faces in combi-... 

The beginning of metal-metal bonding is often seen structurally whenever the stoichiometric number of nonmetals (halides) per metal In a reduced compound Is less than the preferred coordination number so that coordination polyhedra must be shared. Thus, Zrl4 achieves CN6 by sharing two edges of each Zrl0 octahedron, viz, Zrl2l4/2 Only when valence electrons are available does this allow... 

Fig. 12. Octahedral layers of composition MX3 (a) double chains with each octahedron [MXX2/2X3/3] sharing four edges (b) zigzag double chains with one octahedron [MX2/2X4/3] sharing four edges, the neighboring one [MX2X2/2X2/3] sharing only three edges.

It is interesting that rutile, with only two shared edges per octahedron, is reported to be more stable than brookite and anatase, and, moreover, that many substances MXa have the rutile structure, whereas only titanium dioxide has been reported to have the brookite and anatase structures. 

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