Cuboctahedron

When Li metal is cold-worked it transforms from body-centred cubic to cubic close-packed in which each atom is surrounded by 12 others in twinned cuboctahedral coordination below 78 K the stable crystalline modification is hexagonal dose-packed in which each lithium atom has 12 nearest neighbours in the form of a cuboctahedron. This very high coordination... 

Lu Q, Hu J, Tang K, Qian Y, Zhou G, Liu X (2000) Synthesis of nanocrystaUine CuMS2 (M = In or Ga) through a solvothermal process. Inorg Chem 39 1606-1607 Wu C, Yu S-H, Antoniette M (2006) Complex concaved cuboctahedrons of copper sulfide crystals with highly geometrical symmetry created by a solution process. Chem Mater 18 3599-3601... 

Since Ca is not directly surrounded by Ti atoms, the first polyhedron symbol is dropped however, the first comma cannot be dropped to make it clear that the 12co refers to a cuboctahedron formed by 12 O atoms. Ti is not directly surrounded by Ca, but by six O atoms forming an octahedron. O is surrounded in planar (square) coordination by four Ca, by two linearly arranged Ti and by eight O atoms forming a prism. 

A more detailed analysis of the first sphere of 12 Ga atoms shows that the cluster bears a resemblance not only to the anti-cuboctahedron. In the arrangement... 

Figure 4.9 Clusters in the fluorite structure (a, b) transformation of a cube into a square antiprism (c, d) transformation of a cube into a cuboctahedron (e) a single square antiprism formed by tbe creation of < 110> interstitial defects (/) an M6F36 cluster in a fluorite structure matrix. Cations in the plane of tbe section are represented by smaller spheres anions above and below the plane are represented by larger spheres.

Figure 9.34 The typical coordinating polyhedra for a dense regular monospheres packing (a) cuboctahedron, (b) anticuboctahedron, (c) dodecahedron, and (d) icosahedron.

Fig. 3.6-9. Representation of the cluster core of [C PSiBuhk 31. The black spheres (Cu atoms) form a cuboctahedron, the grey spheres (P atoms) an octahedron. The white spheres...

If we have N hard spheres (of radius rs) forming a close-packed polyhedron, another sphere (of smaller radius rc) can fit neatly into the central hole of the polyhedron if the radius ratio has a well-defined value (see also 3.8.1.1). The ideal radius ratio (rc/rs) for a perfect fit is 0.225.. (in a regular tetrahedron, CN 4), 0.414.. (regular octahedron CN 6), 0.528.. (Archimedean trigonal prism CN 6), 0.645... (Archimedean square antiprism CN 8), 0.732.. (cube CN 8), 0.902... (regular icosahedron CN 12), 1 (cuboctahedron and twinned cuboctahedron CN 12). 

Fig. 9.9 The 13 Archimedean solids, in order of increasing number of vertices. Truncated tetrahedron (1), Cuboctahedron (2), Truncated cube (3), Truncated octahedron (4), Rhombicubocta-hedron (5), Snub cube (6), Icosidodecahedron (7),...

Rhombitruncated cuboctahedron (8), Truncated dodecahedron (9), Truncated icosahedron (10), Rhombicosidodecahedron (11), Snub dodecahedron (12), Rhombitruncated icosidodecahedron (13) (see also Table 9.2). 

Fig. 9.15 A theoretical organic shell based upon the cuboctahedron (X = O, S).

Table 1. Calculated Values of the Effect of Particle Size on the Fraction of Atoms on the Surface and First Shell Coordination Numbers (CN) for Cuboctahedron (A/ cuboct) and Icosahedron (Alices) Models for Pt Clusters ...

Figure 16. Icosahedron (left) and cuboctahedron (right) with 147 atoms corresponding to four complete shells. The numbers indicate the first shell coordination numbers of the surface atom sites.(Reproduced with permission from ref 59. Copyright 1992 Royal Society of Chemistry.)...

---