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8 h 2 0,£,z; O,J,z; i,O,z; i,O,z. 8 g 2 x,O,J; 8 / 4 4 ^ 2 e mm 0,0,z; 0,0,z. / 4 O,J,J; i,O,J. i,0,0. <• 222 0,J,0; 2 6 42m 0,0,J. 2 a 42m 0,0,0. hkl: /=2/i xfi,l; x,0,0; Jc,O,O; 4 no extra conditions ,0; 0,Jc,0. no extra conditions hkl: l=2n; (h+k=2n) no extra conditions Figure 1-38. Representation of the space group 142m in the International Tables for Crystallography. Top line: crystal system, point group, full Hermann-Mauguin symbol, space-group number, short symbol, Schonflies symbol. Left drawing: orbit of a point in a general position.
The point form of a point group corresponds to the orbit of a space group (see Sec. 4). If the point group is acting on a crystal face (hkl) a crystal form {hkl} is generated. General and special crystal forms are defined analogously to the point form. The faces of a general crystal form have an eigensymmetry of 1, those of a special one show higher eigensymmetry. The action of the group mm! leads, for a face (h k I) in a general position, to the set of equivalent faces: {hkl), (hkl\ (hkl), (hkl) corresponding to a rhombic pyramid {hkl}.
Triacontahedron with icosahedral point symmetry. 6 Quasicrystals Figure 1-41. , 1989). 49 also possible, of course, to index the faces on a 3-D basis but the indices (h1h2h3) then correspond to irrational numbers. The formation of crystal forms follows the same principles of morphological importance as found for regular crystals: the faces with the shortest normal vectors /J, corresponding to the largest interplanar spacings and connected to the highest density of lattice points, show the highest frequencies.