Crystal symmetries icosahedral packing

Note that the low-temperature structure is neither a quasicrystal nor an icosahedral glass. Given the molecular symmetry, one might have predicted the latter, whereas icosahedral quasicrystals require two distinct structural units to satisfy space filling. While the precise energetic requirements for crystal versus icosahedral glass formation are not understood, it seems likely that the structural order at low T is driven both by a preference for close packing and,by local orientational order. 

FIG. 2. A complex of twenty Friauf polyhedra, with icosahedral symmetry (Samson, Ref. 23). This complex contains 104 atoms, if the central icosahedral position is not occupied. Most of the atoms show approximate icosahedral ligan-cy twenty atoms, at the centers of the Friauf polyhedra, have ligancy 15 or 16. The complex was first identified in Mg32(Al,Zn)<9. In the cubic crystals that form the icosatwins and decatwins these complexes are packed in such a way as to approximate an icosahedral arrangement of twelve complexes about a central one, the structure being similar to that of 0-W. 

Icosahedral and decagonal quasicrystals of intermetallic compounds are multiple twins of cubic or orthorhombic crystals composed of very large atomic complexes with icosahedral point-group symmetry in cubic close packing Structure of decagonal AlePd. Proc. Natl. Acad. Sci. 86 (1989) 9637-9641. 

The use of the rotation function to study the arrangement of subunits in spherical viruses has led to some interesting discussion. A preliminary analysis of the X-ray data on the satellite tobacco necrosis virus crystals indicated that these might have octahedral rather than icosahedral symmetry. However, all solutions to the rotation function originally considered involved a particle two-fold axis parallel to the monoclinic two-fold axis. It has been demonstrated that if this restriction is relaxed, octahedral symmetry is generated in the Patterson by the packing of two virus particles of icosahedral symmetry, This special icosahedral solution appears to be definitely preferable to the octahedral solution. 

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