Icosahedra

The icosahedron consists of 20 deformed tetrahedral sub-units. Here the deformation is placed such that the three edges x1 at the surface (cf. Fig. 13b), which terminate one of the 20 triangular (111) surface planes, are larger by 5% than the others. The magic numbers are the same as for the cuboctahedron, that is, 13, 55, 147, 309,____The tetrahedral angle is again 2p = 72°.

d111 = ax1 cos p' d200 = ax1/{2t§p), a = a x1 = x2^j4 sin2 p — 1 / sin p, x2 = 1.

A model is shown in Figure 15 that consists of five shells (561 atoms). Computer simulations for seven-shelled Cu icosahedra (1415 atoms) together with experimental images and PS are shown in Figures 16-18 in the 5-fold, 3-fold,

Figure 11. Computer simulation and PS of a CdS cluster in cubic structures with stacking faults in the [111] orientation (a-d) and pure hexagonal structure in the [001] orientation (e). The stapling is: (a) abc abc abc, (b) abc abc ab, (c) abc ab ab, (d) ab ab ab, (e) ab ab ab (from top to bottom).

Figure 12. Model of a nontruncated decahedron.
Figure 13. Deformed tetrahedral subunits for the construction of (a) the decahedron and (b) the icosahedron.
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