Crystal symmetries planar networks

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. 

Figure 8.66 Projection along c showing the nearly planar guanidinium-carbonate (1 1) rosette network II at z = 1/2 in the crystal structure of 35. The atom types are differentiated by size and different grey scales, and N-H- O hydrogen bonds are represented by dotted lines. The layer is composed of independent carbonate ions [labeled by their central carbon atoms C(1) and C(3)[ andguanidinium ions [C(2) and C(4)[ in equal numbers. Note Mean atomic deviation from plane of one rosette = 0.36 A, and mean atomic deviation from plane of ribbon fragment [C(1), C(2), C(3), C(4)[ = 0.44 A]. Symmetry transformation a (1 — x, I + y, 1 - z)...

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