In crystallography, the trigonal crystal system is one of the seven crystal systems, and the rhombohedral lattice system is one of the seven lattice systems. They are often confused with each other: crystals in the rhombohedral lattice system are always in the trigonal crystal system, but some crystals such as quartz are in the trigonal crystal system but not in the rhombohedral lattice system. The rhombohedral lattice system consists of the rhombohedral lattice, while the trigonal crystal systems consists of the 5 point groups of the 7 space groups with a rhombohedral lattice. There are 25 space groups whose point groups are one of the 5 in the trigonal crystal system, consisting of the 7 space groups associated with the rhombohedral lattice system together with 18 of the 45 space groups associated with the hexagonal lattice system.
"Rhombohedral crystal system" is an ambiguous term that confuses the trigonal crystal system with the rhombohedral lattice system and may mean either of them (or even the hexagonal crystal family.
In the classification into 6 crystal families, the trigonal crystal system is combined with the hexagonal crystal system and grouped into a larger hexagonal family.[1]
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Rhombohedral lattice system
A lattice system is described by three basis vectors. In the rhombohedral system, the crystal is described by vectors of equal length, none of which are orthogonal. The rhombohedral system can be thought of as the cubic system stretched diagonally along a body. a = b = c; 
. In some classification schemes, the rhombohedral lattice system is combined with the hexagonal lattice system and grouped into a larger hexagonal family.
There is only one rhombohedral Bravais lattice.
List of rhombohedral space groups
The 7 space groups associated to the rhombohedral lattice system are listed below, with their international number and name, followed by their point groups in name and international notation (Hermann-Mauguin notation) and Schoenflies notation, and example crystals. (All these point groups are also associated to some space groups not in the rhombohedral lattice system.)
| Number | Space group | Point group | international | Schoenflies | examples |
|---|---|---|---|---|---|
| 146 | R3 | rhombohedral tetartohedral | 3 | C3 | carlinite |
| 148 | R3 | rhombohedral tetartohedral | 3 | S6 | dolomite |
| 155 | R32 | trapezohedral | 32 | D3 | abhurite |
| 160 | R3m | rhombohedral hemimorphic | 3m | C3v | schorl |
| 161 | R3c | rhombohedral hemimorphic | 3m | C3v | cerite |
| 166 | R3m | rhombohedral holohedral | 3m | D3d | antimony |
| 167 | R3c | rhombohedral holohedral | 3m | D3d | hematite, corundum |
Trigonal crystal system
The trigonal crystal system is the only crystal system whose point groups have more than one lattice system associated with their space groups: the hexagonal and rhombohedral lattices both appear.
The 5 point groups in this crystal system are listed below, followed by their representations in international notation (Hermann-Mauguin notation) and Schoenflies notation, and example crystals.[2][1]
| Class name | international | Schoenflies | examples |
| Hexagonal Scalenohedral |  |
D3d | calcite, corundum, hematite |
| Ditrigonal Pyramidal | 3m | C3v | tourmaline, alunite |
| Rhombohedral |  |
S6 | dolomite, ilmenite |
| Trapezohedral | 32 | D3 | quartz, cinnabar |
| Pyramidal | 3 | C3 | jarosite |
See also
References
- ^ a b Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 78 - 89, ISBN 0-471-80580-7
- ^ http://webmineral.com/crystall.shtml Crystallography and Minerals Arranged by Crystal Form Webmineral
- Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 78 - 89, ISBN 0-471-80580-7
External links
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