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 Results for DC.creator="H." AND DC.creator="Klapper" in section 3.2.1 of volume A   page 1 of 2 pages.
Crystallographic and noncrystallographic point groups
Hahn, Th. and Klapper, H.  International Tables for Crystallography (2016). Vol. A, Section 3.2.1, pp. 720-737 [ doi:10.1107/97809553602060000930 ]
... brief introduction to point-group symbols is provided in Hahn & Klapper (2005 ). General symbol Crystal system Triclinic Monoclinic (top) Orthorhombic ... variation of the values and signs of the Miller indices h, k, l or the point coordinates x, y, z. It ... to the well known `law of rational indices', the indices h, k, l must be integers; no such restrictions apply ...

The two icosahedral groups
Hahn, Th. and Klapper, H.  International Tables for Crystallography (2016). Vol. A, Section 3.2.1.4.2, pp. 733-735 [ doi:10.1107/97809553602060000930 ]
... around a fivefold axis parallel to . The resulting indices h, k, l and coordinates x, y, z are irrational but ... For the geometry of polyhedra, the well known books by H. S. M. Coxeter (especially Coxeter, 1973 ) are recommended. References Coxeter, H. S. M. (1973). Regular Polytopes, 3rd ed. New ...

Description of general point groups
Hahn, Th. and Klapper, H.  International Tables for Crystallography (2016). Vol. A, Section 3.2.1.4.1, pp. 731-733 [ doi:10.1107/97809553602060000930 ]
Description of general point groups 3.2.1.4.1. Description of general point groups In Sections 3.2.1.2 and 3.2.1.3 , only the 32 crystallographic point groups (crystal classes) are considered. In addition, infinitely many noncrystallographic point groups exist that are of interest as possible symmetries of molecules and of quasicrystals and as approximate local site ...

Noncrystallographic point groups
Hahn, Th. and Klapper, H.  International Tables for Crystallography (2016). Vol. A, Section 3.2.1.4, pp. 731-737 [ doi:10.1107/97809553602060000930 ]
... around a fivefold axis parallel to . The resulting indices h, k, l and coordinates x, y, z are irrational but ... For the geometry of polyhedra, the well known books by H. S. M. Coxeter (especially Coxeter, 1973 ) are recommended. 3.2.1.4.3. Sub ... the two-dimensional examples in Fig. 3.2.1.5 ). References Coxeter, H. S. M. (1973). Regular Polytopes, 3rd ed. New ...

Subgroups and supergroups of the crystallographic point groups
Hahn, Th. and Klapper, H.  International Tables for Crystallography (2016). Vol. A, Section 3.2.1.3, p. 731 [ doi:10.1107/97809553602060000930 ]
... A1, Symmetry Relations Between Space Groups, 2nd ed., edited by H. Wondratschek & U. Müller. Chichester: Wiley.GoogleScholar International Tables for Crystallography ...

Names and symbols of the crystal classes
Hahn, Th. and Klapper, H.  International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.5, pp. 730-731 [ doi:10.1107/97809553602060000930 ]
Names and symbols of the crystal classes 3.2.1.2.5. Names and symbols of the crystal classes Several different sets of names have been devised for the 32 crystal classes. Their use, however, has greatly declined since the introduction of the international point-group symbols. As examples, two sets (both translated into English ...

Notes on crystal and point forms
Hahn, Th. and Klapper, H.  International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.4, pp. 729-730 [ doi:10.1107/97809553602060000930 ]
... Section 3.2.1.4.2 and listed in Table 3.2.2.1 . References Burzlaff, H. & Zimmermann, H. (1977). Symmetrielehre, especially ch. II.3. Stuttgart: Thieme.GoogleScholar Fischer, W., Burzlaff, H., Hellner, E. & Donnay, J. D. H. (1973). Space ...

Description of crystal and point forms
Hahn, Th. and Klapper, H.  International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.3, pp. 727-729 [ doi:10.1107/97809553602060000930 ]
... X-ray (neutron) reflections. This important aspect is treated in Klapper & Hahn (2010 ). Examples (1) In point group , the general ... is concerned can be found in Section 3.2.4.3 . References Klapper, H. & Hahn, Th. (2010). The application of eigensymmetries of ...

Crystal and point forms
Hahn, Th. and Klapper, H.  International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.2, pp. 722-727 [ doi:10.1107/97809553602060000930 ]
... variation of the values and signs of the Miller indices h, k, l or the point coordinates x, y, z. It ... to the well known `law of rational indices', the indices h, k, l must be integers; no such restrictions apply to ...

Description of point groups
Hahn, Th. and Klapper, H.  International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.1, pp. 721-722 [ doi:10.1107/97809553602060000930 ]
Description of point groups 3.2.1.2.1. Description of point groups In crystallography, point groups usually are described (i) by means of their Hermann-Mauguin or Schoenflies symbols; (ii) by means of their stereographic projections; (iii) by means of the matrix representations of their symmetry operations, frequently listed in the form of Miller ...

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