Schonflies symbol

Arthur Moritz SchOnflies, German mathematician (1853-1928). The SchOnflies symbols are employed io spectroscopic applications, while in crystallography the international, or Hennann-Maugiur) notation is used. 

In the top row are these entries In the upper left comer is the Schonflies symbol for the group. Then, along the top row of the main body of the table, are listed the elements of the group, gathered into classes the notation is the kind explained in Section 3.13. 

Second, there are five rotoinversion operations, symbolized 1, 2, 3, 4, and 6. We need to examine these more closely to see how they relate to the Schonflies symbols 5, m, and / (where it is well to recall that m = Sx and / s S2). 

Let us now look more closely at these 32 point groups, for each of which Table 11.3 gives both the familiar Schonflies symbol and the crystallographic one. For many of the simpler cases we have already discussed the basis for the crystallographic symbol, but it is worthwhile to do this for a few more. 

Number Schonflies Symbol Crystallographic Costal Symbol System ... 

Schonflies symbol Full International symbol Abbreviated symbol... 

Laue symmetry is 2/m (disregarding the translational components of the 21-axis and the c glide), so the space group belongs to the monoclinic system. The simplified symbol P2 /c normally replaces the full symbol P 2 /c, and the old Schonflies symbol C A (the fifth space group derived from the point group C2h) is seldom used. 

Headline. Provides the short international (Hermann-Mauguin) space group symmetry symbol (Cmm2) followed by the SchOnflies symbol of... 

Figure 4.10 Flow chartfor the determination of point groups (Schonflies symbols, n = 2,3,...). To find the point group of a given object, answer questions working downwards follow the full line to the right if the answer is Yes or the dashed line to the left if it is No...

Generally, there is infinite number of point groups, but not all of them correspond to real physical objects such as molecules or crystals. For example, only 32 point groups are compatible with crystal lattices. Each of them is labeled by a certain symbol according to Schonflies or according to the International classifications. The Schonflies symbols are vivid and more often used in scientific literature. Here we present only those point groups we may encounter in the literature on liquid crystals. 

Lattice system Bravais lattices Schonflies symbol Hermann-Mauguin Properties... 

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