Symmetry decagonal

Fig. 10.7. (Eight) Simulation showing tenfold symmetry decagonal quasi crystals...

A little later (Bendersky 1985, Chattopadhyay et al. 1985) decagonal (tenfold) symmetry was discovered in other Al-transition metal compounds quasiperiodic layers are stacked periodically in the third dimension. Since then, one or other of these forms of quasicrystal have been identified in many different compositions. A detailed review of the decagonal type is by Ranganathan et al. (1997). 

Ten H atoms in a decagonal geometry of Du, symmetry and the RA and RB variables. Again, we determine only the saddle point. 

At present, a number of quasi-crystalline alloys with icosahedral, decagonal, and octagonal symmetry are synthesized by different methods. The quasicrystalline form of the solids turned out to be widespread in a great extent. The absence of the translation symmetry and the presence of numerous interstitial sites of the different types in the structure of icosahedral quasicrystals makes some of them interesting objects for hydride chemistry. We cannot wait for any sensational discoveries here, as the general laws of M-H interaction do not depend on matrix structure. However, encouraging results were obtained for icosahedral Ti45Zr38Nii7... 

Some stable ternary intermetallic phases have been found that are quasiperi-odic in two dimensions and periodic in the third. These are from the systems Al—Ni—Co, Al—Cu—Co, and Al—Mn—Pd. They contain decagonally packed groups of atoms (local tenfold rotational symmetry). It should be noted that there are also known metastable quasicrystals with local eightfold rotational symmetry (octagonal) and 12-fold rotational symmetry (dodecagonal) as well. The dodecahedron is also one of the five Platonic solids (Lalena and Cleary, 2005). 

L. Pauling, Interpretation of so-called icosahedral and decagonal quasicrystals of alloys showing apparent icosahedral symmetry elements as twins of an 820-atom cubic crystal. Computers Math. Applic. 17, 337-339 (1989). 

The figure displays the 120-vertex equilateral regular orbit cage of Ih point symmetry. The locations of the poles of the rotational axes are marked on the projection and the vertices are divided into sets of decagons of different colours. The orbit cage is 3-valent, which means that there are 3 connections about each vertex contributing to the net of the structure. 

Whether quasicrystalline structures are limited to alloys remains an open question. It is possible that their occurrence is much more widespread than had been previously thought. Indeed there is evidence for quasicrystallinity in both thermotropic and lyotropic liquid crystals. Diffraction patterns of decagonal symmetry have been recorded in lyotropic liquid crystals [K. Fontell, private communication], (Fig. 2.19), and there is theoretical evidence for the existence of a quasicrystalline structure within the blue phase of cholesterol (Chapters 4, 5). (The decagonal structure has quasisymmetry perpendicular to the tenfold axes, and translation symmetry along them.) Viruses crystallise in icosahedral clusters and the list continues to grow. In addition to five-fold symmetry, it has been shown that eight and ten- fold quasisymmetry is possible. ... 

We think that the structural principles that imderlie quasicrystals (discussed in Chapter 2) are relevant in order to describe the superstructure of tropocollagen molecules, which must accommodate the wide variety of tissue structures that can be formed. There are no possibilities of packing triple helices in a space-filling arrangement. A structure with five-fold symmetry in the plane and with perfect periodicity in the perpendicular direction, however, which is consistent with the quarter stagger pentafibril model, is in fact a quasicrystal of so-called T-type (also known as the decagonal phase). 

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. 

To date, aU known 2-D quasiperiodic materials exhibit noncrystallographic diffraction symmetries of 8/mmm, 10/mmm, or 12/mram. The structures of these materials are called octagonal, decagonal, and do-decagonal structures, respectively. Quasiperiodicity is present only in planes stacked along a perpendicular periodic direction. To index the lattice points in a plane, four basis vectors a, 2. 4 are needed a fifth one,... 

The majority of known metallic QCs have one of two types of structures icosahedral and decagonal. In icosahedral materials, the highest symmetry axis is fivefold. The icosahedral (i-)QCs can essentially be considered quasiperiodic in three dimensions. In decagonal materials, the highest symmetry axis is 10-fold. 

Decagonal Pseudo-Symmetry , Acta Crystallogr., B51, 31-36 (1995) (Crys. Structure, Experimental, 28)... 

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