Tetrahedron truncated

Two limiting structures with four spherons as core or inner core are shown in Figs. 6 and 7. The structure shown in Fig. 6 has the central tetrahedron of four spherons surrounded by a larger tetrahedron of four and a truncated tetrahedron of 12, a total of 16 spherons in the outer layer. The packing is triangular. This is the structure of the cpre for magic number 126. It has double completed-shell character, LN. 

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),...

Fujita et al., [37] Stang et al., [38] and Steel et al. [39] have recently described the synthesis of MSL4 cages which are topologically analogous to a truncated tetrahedron (Fig. 9-14). These systems, which may be regarded as inverted M4L6 frame-... 

Flg. 9.14. Fujita s metal-based cage, a host based upon the truncated tetrahedron. 

Zubieta et al. have also demonstrated the formation of a cage topologically equivalent to a truncated tetrahedron, [Moi6(OH)1204o]8. Composed of four Mo(VI) and twelve Mo(V) centers, this host possesses a central [Moi204o]20 core which encapsulates a proton or sodium ion. [40]... 

Fig. 26. Y-Fe2Si04 (high-pressure spinel form) projected on (001) of the cubic cell Fe and Si atoms only. Large circle = Si, small circle = Fe, heights in units of c/8. The f.c.c. unit cell is dotted, the equivalent b.c.t. unit cell (c, = cj outlined with broken lines. The SiFci2 truncated tetrahedra are drawn top right. Si at 3/4 bottom right. Si at 1/2 bottom left. Si at 1/4 top left. Si at 0. (Note that the Fe which appear to be at the centres of hexagonal faces are not. They form the lower edge of the truncated tetrahedron concerned.)...

The large Mg atom has CN 16. Twelve M atoms (Cu, Zn, or Ni) form a truncated tetrahedron seen in Figure 9.43. The CN 16 is completed by four tetrahedrally arranged Mg atoms through the triangular faces. 

Figure 9.43. The truncated tetrahedron, the cage for Mg, in Laves phases.

Figure 7. The Friauf polyhedron. It consists of 12 smaller atoms at the comers of a truncated tetrahedron, which has four hexagonal faces and four triangular faces, and a larger atom at the center. In condensation, hexagonal faces are shared.

Hence, we suggest the following model of Zn O nucleus-clusters. The nucleus-cluster has the shape of the truncated tetrahedron with 12 atoms of zinc and one atom of oxygen in the center (inset of Fig. 1). Such nucleus-cluster is a loosely coupled system formed by an atom of oxygen and 12 equidistant atoms of zinc. Scattering in zinc vapor at increased partial pressure of oxygen, facilitates the nucleation and growth of (OOOl)ZnO whiskers on four facets of the Zn O cluster occurs. 

The general object with 12 vertices, the regular orbit of the T group is shown in Figure 2.17a as an elliptical projection and in perspective, as the distorted truncated tetrahedron in Figure 2.17b. The only other non-trivial orbit for structures of T symmetry, is the simple tetrahedron, realized collapse of the local sets onto the poles of the three-fold rotational axes. 

Truncated tetrahedron (TT) Truncated cube(TC) Truncated octahedron(TO)... 

The complexity order of Archimedean solids in terms of the solid angle of their vertices is280 TT < CO < TC < TO < RCO < ID < TCO < TD < TCO < RID < TID. The two chiral Archimedean solids (snub octahedron, snub icosidodecahedron) were not considered. This order disagree with all four complexity given above, except in the case of the truncated tetrahedron which is predicted to be the least complex of all Archimedean solids. This discrepancy is perhaps due to different bases of the compared complexity orders the above orders being the result of 2D representation and the Balaban-Bonchev order of 3D structure of Archimedean solids. 

Three or more molecules may assemble in the solid state to form a finite assembly with connecting forces propagated in 3D. The components of such an assembly will typically form a polyhedral shell. The shell may accommodate chemical species as guests. The polyhedron may be based on a prism or antiprism, as well as one of the five Platonic (e.g. cube, tetrahedron) or 13 Archimedean (e.g. truncated tetrahedron) solids.4... 

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