|
The following table lists the notations for the
thirty-two crystallographic point group,
organized by crystal system [1,2].
The Hermann-Mauguin System is often
referred to as the International System.
This convention is commonly applied to the decription of
crystallographic point and space groups in solid-state
chemistry and materials science.
The Schoenflies notation system has often
been (and still is) used to describe the symmetry of
molecules [3].
|
| Crystal system |
Hermann-Mauguin notation |
Schoenflies notation |
| Triclinic |
1 |
C1 |
| 1 |
Ci |
| Monoclinic |
2 |
C2 |
| m |
Cs |
| 2/m |
C2h |
| Orthorhombic |
222 |
D2 |
| mm2 |
C2v |
| mmm |
D2h |
| Tetragonal |
4 |
C4 |
| 4 |
S4 |
| 4/m |
C4h |
| 422 |
D4 |
| 4mm |
C4v |
| 42m |
D2d |
| 4/m mm |
D4h |
| Trigonal |
3 |
C3 |
| 3 |
C3i |
| 32 |
D3 |
| 3m |
C3v |
| 3m |
D3d |
| Hexagonal |
6 |
C6 |
| 6 |
C3h |
| 6/m |
C6h |
| 622 |
D6 |
| 6mm |
C6v |
| 6m2 |
D3h |
| 6/m mm |
D6h |
| Cubic |
23 |
T |
| m3 |
Th |
| 432 |
O |
| 43m |
Td |
| m3m |
Oh |
|
The numbers and letters in a Hermann-Mauguin notation encode
point symmetry elements [2]:
| - the rotation axes 1, 2, 3, 4, and 6; |
| - the inversion axes
1,
2,
3,
4, and
6;
|
| - the mirror plane m (equivalent to
2).
|
|
References and Notes
| [1] |
Gregory S. Rohrer:
Structure and Bonding in Crystalline Materials,
Cambridge University Press,
Cambridge, UK,
2001.
See Chapter 3 Symmetry in Crystal Structures
and Table 3.1 therein.
|
| [2] |
Anthony R. West:
Solid State Chemistry and Its
Applications,
John Wiley & Sons,
Chichester,
1984.
See Chapter 6 Point Groups, Space Groups and Crystal
Structure
and Table 6.2 therein.
|
| [3] |
David M. Bishop:
Group Theory and Chemistry,
Dover Publications, Inc.,
New York,
1973.
|
|
|
