Symmetry planar networks

Figure 8-24. The 17 symmetry classes of one-sided planar networks with the most important symmetry elements and the notations of the classes indicated. Along with the geometrical configurations, Hungarian needlework patterns are presented for illustration. A brief description of the origin of these patterns is given here [36] ...

Figure 8-25. Scheme for establishing the symmetry of planar networks after Crowe [37],... 

Figure 9-16. Planar networks of regular polygons with up to eight-fold symmetry.

To have 32 symmetry classes for the external forms of crystals is a definite restriction, and it is obviously the consequence of inner structure. The translation periodicity limits the symmetry elements that may be present in a crystal. The most striking limitation is the absence of fivefold rotation in the world of crystals. Consider, for example, planar networks of regular polygons (Figure 9-16). Those with threefold, fourfold, and sixfold symmetry cover the... 

Crystal structures of two hexitols, galactitol and D-mannitol, have been published. Galactitol is meso, but the permissible intramolecular center of symmetry is not utilized in the crystal.28 The molecules crystallize as enantiomorphic pairs that, in conformation, are almost centrosymmetric molecules the difference therefrom is of the same order of magnitude as the thermal motion of the atoms. The carbon atoms and terminal oxygen atoms form an approximately planar chain. All of the oxygen atoms are both donors and acceptors for an intricate network of hydrogen bonding. 

By decoration of these various infinite two-dimensional manifolds (just as the sphere has been decorated with closed networks) several related structures have been proposed for graphite nets. These are mostly based on the P, D and G surfaces (the first two due to Schwarz (1890) and the last, the gyroid, discovered by Schoen (1970). However, many other surfaces (perhaps 50) are available for consideration. Some fit naturally with hexagonal sheets and others with sheets of square or lower symmetry. In general, the P, D and G surfaces are the least curved from planarity. Surfaces parallel to the surfaces of zero mean curvature have lower symmetry than those with H = 0. When decorated with graphite nets the symmetry may be further lowered to that of a sub-group of the symmetry group of the surface itself. 

Fig. 23.8. Structure of the solvent network located in the cavity between the two subunits of glutathione reductase. Water molecules indicated by circles, amino acids by boxed numbers with functional main-chain or side-chain atoms indicated. Hydrogen bonds marked by solid or dashed lines, distances in A units, the twofold symmetry axis is shown An X indicates a solvent molecule s3.5 A away from one of the featured solvent molecules. Pentagonal (except W38) and quadrilateral arrangements are nearly planar, angles between the planes are AB =115°, AC = 125 °, CD = 120°, DE = 125 0 [842]...

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