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Crystallographic and noncrystallographic point groups
International Tables for Crystallography (2016). Vol. A, Section 3.2.1, pp. 720-737 [ doi:10.1107/97809553602060000930 ]
... A brief introduction to point-group symbols is provided in Hahn & Klapper (2005). General symbolCrystal system TriclinicMonoclinic (top) Orthorhombic (bottom ... ray (neutron) reflections. This important aspect is treated in Klapper & Hahn (2010). Examples (1) In point group , the general crystal ... Strasbourg: Berger-Levrault. [Reprinted (1964). Paris: Blanchard.] Klapper, H. & Hahn, Th. (2010). The application of eigensymmetries of face ...
The two icosahedral groups
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.4.2, pp. 733-735 [ doi:10.1107/97809553602060000930 ]
The two icosahedral groups 3.2.1.4.2. The two icosahedral groups The two point groups 235 and of the icosahedral system (orders 60 and 120) are of particular interest among the noncrystallographic groups because of the occurrence of fivefold axes and their increasing importance as symmetries of molecules (viruses), of quasicrystals, and as ...
Description of general point groups
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
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.4, pp. 731-737 [ doi:10.1107/97809553602060000930 ]
Noncrystallographic point groups 3.2.1.4. Noncrystallographic 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 ...
Subgroups and supergroups of the crystallographic point groups
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.3, p. 731 [ doi:10.1107/97809553602060000930 ]
Subgroups and supergroups of the crystallographic point groups 3.2.1.3. Subgroups and supergroups of the crystallographic point groups In this section, the sub- and supergroup relations between the crystallographic point groups are presented in the form of a `family tree'.12 Figs. 3.2.1.2 and 3.2.1.3 apply to two and three dimensions. The ...
Names and symbols of the crystal classes
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
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.4, pp. 729-730 [ doi:10.1107/97809553602060000930 ]
Notes on crystal and point forms 3.2.1.2.4. Notes on crystal and point forms (i) As mentioned in Section 3.2.1.1, each set of Miller indices of a given point group represents infinitely many face forms with the same name. Exceptions occur for the following cases. Some special crystal forms occur with only ...
Description of crystal and point forms
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.3, pp. 727-729 [ doi:10.1107/97809553602060000930 ]
... ray (neutron) reflections. This important aspect is treated in Klapper & Hahn (2010). Examples (1) In point group , the general crystal ... concerned can be found in Section 3.2.4.3. References Klapper, H. & Hahn, Th. (2010). The application of eigensymmetries of face forms ...
Crystal and point forms
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.2, pp. 722-727 [ doi:10.1107/97809553602060000930 ]
Crystal and point forms 3.2.1.2.2. Crystal and point forms For a point group a crystal form is a set of all symmetry-equivalent faces; a point form is a set of all symmetry-equivalent points. Crystal and point forms in point groups correspond to `crystallographic orbits' in space groups; cf. Sections ...
Description of point groups
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 ...
International Tables for Crystallography (2016). Vol. A, Section 3.2.1, pp. 720-737 [ doi:10.1107/97809553602060000930 ]
... A brief introduction to point-group symbols is provided in Hahn & Klapper (2005). General symbolCrystal system TriclinicMonoclinic (top) Orthorhombic (bottom ... ray (neutron) reflections. This important aspect is treated in Klapper & Hahn (2010). Examples (1) In point group , the general crystal ... Strasbourg: Berger-Levrault. [Reprinted (1964). Paris: Blanchard.] Klapper, H. & Hahn, Th. (2010). The application of eigensymmetries of face ...
The two icosahedral groups
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.4.2, pp. 733-735 [ doi:10.1107/97809553602060000930 ]
The two icosahedral groups 3.2.1.4.2. The two icosahedral groups The two point groups 235 and of the icosahedral system (orders 60 and 120) are of particular interest among the noncrystallographic groups because of the occurrence of fivefold axes and their increasing importance as symmetries of molecules (viruses), of quasicrystals, and as ...
Description of general point groups
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
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.4, pp. 731-737 [ doi:10.1107/97809553602060000930 ]
Noncrystallographic point groups 3.2.1.4. Noncrystallographic 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 ...
Subgroups and supergroups of the crystallographic point groups
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.3, p. 731 [ doi:10.1107/97809553602060000930 ]
Subgroups and supergroups of the crystallographic point groups 3.2.1.3. Subgroups and supergroups of the crystallographic point groups In this section, the sub- and supergroup relations between the crystallographic point groups are presented in the form of a `family tree'.12 Figs. 3.2.1.2 and 3.2.1.3 apply to two and three dimensions. The ...
Names and symbols of the crystal classes
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
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.4, pp. 729-730 [ doi:10.1107/97809553602060000930 ]
Notes on crystal and point forms 3.2.1.2.4. Notes on crystal and point forms (i) As mentioned in Section 3.2.1.1, each set of Miller indices of a given point group represents infinitely many face forms with the same name. Exceptions occur for the following cases. Some special crystal forms occur with only ...
Description of crystal and point forms
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.3, pp. 727-729 [ doi:10.1107/97809553602060000930 ]
... ray (neutron) reflections. This important aspect is treated in Klapper & Hahn (2010). Examples (1) In point group , the general crystal ... concerned can be found in Section 3.2.4.3. References Klapper, H. & Hahn, Th. (2010). The application of eigensymmetries of face forms ...
Crystal and point forms
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.2.2, pp. 722-727 [ doi:10.1107/97809553602060000930 ]
Crystal and point forms 3.2.1.2.2. Crystal and point forms For a point group a crystal form is a set of all symmetry-equivalent faces; a point form is a set of all symmetry-equivalent points. Crystal and point forms in point groups correspond to `crystallographic orbits' in space groups; cf. Sections ...
Description of point groups
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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