Icosahedral group

Molecules with icosahedral symmetry are not new but the discovery of the newest of them, Ceo or buckminsterfiillerene, has had such a profound effect on chemistry in recent years that 1 thought it useful fo include a discussion of fhe icosahedral poinf group fo which Ceo belongs. 

Main Group Element Carborane Derivatives. Main group element carborane derivatives have been reviewed (231). Only a few alkaline-earth element metaHacarborane derivatives have been characterized. The icosahedral beryUacarborane, /(9j (9-3-[(CH3)3N]-3,l,2-BeC2B H, shown in Figure 24a, has been prepared via the reaction of nido-1 and Be(CH3)2 [0(C2H3)2]2 followed by reaction of the diethyletherate product and... 

At higher frequencies (above 200 cm ) the vibrational spectra for fullerenes and their cry.stalline solids are dominated by the intramolecular modes. Because of the high symmetry of the Cgo molecule (icosahedral point group Ih), there are only 46 distinct molecular mode frequencies corresponding to the 180 6 = 174 degrees of freedom for the isolated Cgo molecule, and of these only 4 are infrared-active (all with Ti symmetry) and 10 are Raman-active (2 with Ag symmetry and 8 with Hg symmetry). The remaining 32 eigcnfrequencies correspond to silent modes, i.e., they are not optically active in first order. 

An extensive derivative chemistry of the icosahedral carboranes has been developed, especially for l,2-C2BioHi2. Terminal H atoms attached to B undergo facile electrophilic substitution and the sequence of reactivity follows the sequence of negative charge density on the BHt group ... 

Mn(N03)4] , [Fe(N03)4] and [Sn(N03)4], which feature dodecahedral coordination about the metal [Ce(N03)5] in which the 5 bidentate nitrate groups define a trigonal bipyramid leading to tenfold coordination of cerium (Fig. 11.17b) [Ce(N03)6] and [Th(N03)6] , which feature nearly regular icosahedral (p. 141) coordination of the metal by 12 O atoms and many lanthanide and uranyl [U02] complexes. It seems, therefore, that the size of the metal centre is not necessarily a dominant factor. 

Considering the mode of filling the voids in the metal framework of rj phases with the Ti2Ni type (see Ref. 1) (Table 1), Re3Al2B is the only boride member of this group, with B atoms entering the large icosahedral center in 16d, occupied by metal... 

Lithium has been alloyed with gaUium and small amounts of valence-electron poorer elements Cu, Ag, Zn and Cd. like the early p-block elements (especially group 13), these elements are icosogen, a term which was coined by King for elements that can form icosahedron-based clusters [24]. In these combinations, the valence electron concentrations are reduced to such a degree that low-coordinated Ga atoms are no longer present, and icosahedral clustering prevails [25]. Periodic 3-D networks are formed from an icosahedron kernel and the icosahedral symmetry is extended within the boundary of a few shells. 

Picomaviruses Poliovirus Naked icosahedral particles 28 nm in diameter One of a group of enteroviruses common in the gut of humans. The primary site of multiplication is the lymphoid tissue of the alimentary tract. Only rarely do they cause systemic infections or serious neurological conditions like encephalitis or poliomyelitis... 

You have replied that your molecule has a 5-fold axis of rotation. Verify that it also has 15 binary axes and ten ternary axes. Note that it belongs to one of the icosahedral groups. If you play soccer, consider the ball. Before you kick it, look at it. What is its symmetry ... 

Fig. 4 Crystal structures of alS AgTlB (A = K,Rb,Cs), b NauKgTlisM (M = Mg,Zn,Cd,Hg), and c Mg2Zni 1, all of which contain centered icosahedral of the main group elements...

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