Space groups, crystallographic

Table 1. Some crystallographic space groups supporting helical canals...

Crystallographic space groups in which screw axes could describe helical canals are outlined in Table 1, according to the occurrence of surrounding symmetry axes and symmetry axes which intersect the screw axes. 

The extraordinary bonding properties in 16 can also be seen in a diagram of 16 (Fig. 34). In 16, an almost perfect five-numbered axis is attained, distorted only by the central Ga2 unit. This is the first time that a symmetry close to the five-numbered symmetry is observed for molecular metalloid clusters. A few solid-state modifications with five-numbered symmetry have, however, been found for compounds involving Group 13 elements. Because there is no crystallographic space group with a five-numbered axis, these compounds are summarized under the collective name quasi-crystals .83 For a better understanding of quasi-crystals,... 

The group (E, J) has only two one-dimensional irreducible representations. The representations of 0/(3) can therefore be obtained from those of 0(3) as direct products. The group 0/(3) is called the three-dimensional rotation-inversion group. It is isomorphic with the crystallographic space group Pi. 

Single-crystal precession data indicate orthorhombic symmetry with the crystallographic space group Fddd. This system is not isostructural with any other known metal oxyfluoride or metal dioxide. The cell dimensions, determined from Guinier data, are a = 8.370 1 A. b = 10.182 1 A. and c = 7.030 1 A. The indexed powder data are given in reference 6. 

Kovalev, O. V. (1993) Representations of the Crystallographic Space Groups Irreducible Representations, Induced Representations and Corepresentations, 2nd edn. Philadelphia, PA Gordon and Breach. 

Shubnikov, A. V. and Belov, N. V. (1964) Colored Symmetry. Oxford Pergamon Press. Stokes, H. T. and Hatch, D.M. (1988) Isotropy Subgroups of the 230 Crystallographic Space Groups. Singapore World Scientific. 

Combining the five point group symmetry operators with the two translational symmetry operators gives a total of exactly 230 different possible combinations, called the crystallographic space groups. Every crystal... 

Table 4.1 Geometric properties of some periodic minimal surfaces. The "genus" of each three-periodic minimal surface (IPMS) is the genus of a unit cell of the IPMS (with symmetrically distinct sides). The "symmetry" refers to the crystallographic space group for the surface (assuming equivalent sidesl.liie surfaces are tabulated in order of deviation of the homogeneity index from the "ideal" value of 3/4. ...

Isotypy. Isotypic substances are those that have the same crystallographic space group and analogous chemical formulae and crystal structures. The terms isostructural and isomorphic are essentially synonymous with isotypic . 

Homeotypy. Homeotypic substances are those that have similar crystal structures, but with different crystallographic space groups and/or chemical compositions. 

Table 1.17. The 230 crystallographic space groups arranged according to seven crystal systems and 32 crystallographic point groups as they are listed in the International Tables for Crystallography, vol. A. The centrosymmetric groups are in bold, while the non-centrosymmetric groups that do not invert an object are in italic. The remaining are non-...

The international crystallographic space group symbols begin with a capital letter designating Bravais lattice, i.e. P, A, B, C, I, F or R (see Table 1.13 and Table 1.14). 

---