Point Schoenflies symbols

Examples of rotation axes. In each case the Hermann-Mauguin symbol is given on the left side, and the Schoenflies symbol on the right side. tni means point, pronounced dyan in Chinese, hoshi in Japanese... 

Symmetrical geometric figures and their point group symbols in each case, the short Hermann-Mauguin symbol is given to the left, and the Schoenflies symbol to the right... 

Figures 3.8 and 3.9 list point group symbols and illustrate them by geometric figures. In addition to the short Hermann-Mauguin symbols the Schoenflies symbols are also listed. Full Hermann-Mauguin symbols for some point groups are ...

At this point, it is important to mention that, in spite of the great variety of active centers (molecules, ions in solids, color centers, etc.), it can be demonstrated that only 32 point symmetry groups exist in nature. These 32 point symmetry groups (denoted by the so-called Schoenflies symbols) are listed in Table 7.1. The group order and... 

Point-group Hermann-Mattguin syrn bols Schoenflies symbol ... 

Schoenflies symbols are given for all point groups. Hermann/Mauguin symbols are given for the 32 crystallographic point groups. 

The symmetry operators that characterise a point group are collected together into the point group symbol. Crystallographers use the International or Hermann-Mauguin symbols. [The alternative Schoenflies symbols are given in Appendix 3.] As in two-dimensions, the... 

In 1965, Weinreich developed a set of figures which illustrate the 32 point-group symmetries. These are shown in 1.4.16., given on the following page, along with appropriate Schoenflies symbols. 

TABLE 11.3 The 32 crystallographic point groups wKh their Schoenflies and Hermann-Mauguin point group symbols. 

The H-M symbolism derived from crystal symmetry operations. For image and movie representations of each point group, see the website http //cst-www.nrl.navy.mil/lattice/spcgrp/index.html The analogous Schoenflies symbolism derived from molecular symmetry operations. 

A group that consists of point symmetry operations is called a point group. A unique symbol called a Schoenflies symbol is assigned to each point group. The Schoenflies symbol of the point group of the H2O molecule is C2 . This symbol indicates that the molecule has a C2 rotation axis and two vertical mirror planes. You can specify the symmetry properties of a molecule like H2O or SO2 quickly to a knowledgeable person... 

The triclinic system, shovm in Figure 4.10a, has the properties a b c and a /3 y 90° or 120° (where a is the angle between b and c, etc.), and has the least symmetry. It has no rotational symmetry other than the trivial onefold axis of symmetry, meaning that it is necessary to rotate a full 360° about an axis in order to bring all points back into congruence. It does, however, posses a center of inversion. The Schoenflies symbol for this class is Ci, the C for "cyclic" and the subscript 1 indicates ordy an n-fold axis of rotational symmetry in this case n = 1. The international symbol is 1, the bar over the 1 indicating the center of inversion. 

At this point, you may find that the subject of symmetry in a crysted structure to be confusing. However, by studying the terminology carefully in Table 2-2, one can begin to sort out the various lattice structures and the symbols used to delineate them. All of the crystal systems can be described by use of either Schoenflies or Hermaim-Mauguin S5mbols, coupled with the use of the proper geometrical symbols. 

Note 5 From a crystallographic point of view, the uniaxial nematic structure is characterised by the symbol Dooh in the Schoenflies notation (Wmm in the International System). 

The symbols used to designate the elements of molecular point groups in the Schoenflies notation and their descriptions are as follows ... 

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