Octahedron truncated

Sphere Tetrahedron Cube Octahedron Truncated Truncated Truncated Single-crystal... 

Periodic cells used in computer simulations the cube, truncated octahedron, hexagonal prism and rhombic hedron. 

The truncated octahedron and the rhombic dodecahedron provide periodic cells that are approximately spherical and so may be more appropriate for simulations of spherical molecules. The distance between adjacent cells in the truncated octahedron or the rhombic df)decahedron is larger than the conventional cube for a system with a given number of particles and so a simulation using one of the spherical cells will require fewer particles than a comparable simulation using a cubic cell. Of the two approximately spherical cells, the truncated octahedron is often preferred as it is somewhat easier to program. The hexagonal prism can be used to simulate molecules with a cylindrical shape such as DNA. 

Of the five possible shapes, the cube/parallelepiped and the truncated octahedron have been most widely used, with some simulations in the hexagonal prism. The formulae used to translate a particle back into the central simulation box for these three shapes are given in Appendix 6.4. It may be preferable to use one of the more common periodic cells even if there are aesthetic reasons for using an alternative. This is because the expressions for calculating the images may be difficult and inefficient to implement, even though the simulation would use fewer atoms. 

Figure 14.11 Crystal structure of HPF6.6H2O showing the cavity formed by 24 H2O molecules disposed with their O atoms at the vertices of a truncated octahedron, The PFe octahedra occupy centre and comers of the cubic unit cell, i.c. one PFr, at the centre of each cavily. ...

The linking pattern of two zeolites is shown in Fig. 16.24. They have the /I-cage as one of their building blocks, that is, a truncated octahedron, a polyhedron with 24 vertices and 14 faces. In the synthetic zeolite A (Linde A) the /3-cages form a cubic primitive lattice, and are joined by cubes. j3-Cages distributed in the same manner as the atoms in diamond and linked by hexagonal prisms make up the structure of faujasite (zeolite X). 

Figure 11. The truncated octahedron building block (also termed sodalite cage,f or p-cage ) (a) tetrahedral atoms (usually Si or Al) are located at the corners of the polygons with oxygen atoms halfway between them. Illustration of the linkage, through double four-membered rings, of two truncated octahedra (b) and the structure of zeolite-A (c).

These are several Fee structures which are based on the octahedron and are illustrated in Fig. 7. In fact the square pyramid is a half-octahedron. The cubo-octahedron structures are obtained from the octahedron by truncations in 100 planes. It is interesting to note that the polyhedra might have different faces in contact with the substrate. 

In many cases the octahedron based structures appear with a truncation R = 75%. In that case they can be described as platelets. On the other hand the fact that the growth rate of the various crystal faces might be different generates irregular shaped platelets. A particulary common shape are the triangular plates (shown in Fig. 8). These are the result of truncating a single tetrahedron with ill faces. 

D correspondingly, the total number of contacts is HpI=Hp r 1rnP U[C 14. In this case, aPBU has the form of a truncated octahedron with 14 edges (see Figure 9.28c). 

It was indicated above that Ni38 is a special case. Reactivity experiments52 measuring the saturation coverage of this cluster with N2, H2, and CO molecules suggest that the structure of Ni3g is a truncated octahedron cut from a face-centered cubic (fee) lattice. This structure is shown in... 

From a geometrical point of view only, this structure could be compared with that of CsCl, with 1 Ca in place of Cs, and the centre of a 6 B octahedron in place of the Cl atom (in the centre of the cell with its axes parallel to the cell axes). Ca is surrounded by 24 B in a regular truncated cube (octahedra and truncated cubes fill space). A number of hexaborides (of Ca, Sr, Ba, Y and several lanthanides and Th, Np, Pu, Am) have been described as pertaining to this structural type. 

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),...

Kretschmer et al. have described the formation of a lanthanide complex, [Cp6Yb6Cl13] (Cp = cydopentadienyl), which conforms to a truncated octahedron. [36] The anion contains six ytterbium ions, located at the corners of an octahedron, and 12 bridging choride ions. A single chloride ion occupies the center of the shell. 

Octacoordination is often encountered in lanthanide complexes. The preferred poly-hedra for eight coordination expected on the basis of interligand repulsivities are square antiprism (D ), dodecahedron with triangular faces (Z)2d), bicapped octahedron (D3(i), truncated octahedron (Z)2ft), 4,4-bicapped trigonal prism (C2v), distorted cube (C2v), and cube (0/,). The most commonly observed polyhedra for this coordination number are, however, the square antiprism and the dodecahedron. 

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