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# Rhombohedral

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 Title: Rhombohedral Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Rhombohedral

 dolomite quartz

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 system consists of the five point groups of the seven space groups with a rhombohedral lattice. There are 25 space groups whose point groups are one of the five in the trigonal crystal system, consisting of the seven 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]

## 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, no two of which are orthogonal. The rhombohedral system can be thought of as the cubic system stretched along a body diagonal. a = b = c; α = β = γ ≠ 90°. 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.

## 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.

Unit cells for trigonal crystal system
Rhombohedral Hexagonal

The 5 point groups in this crystal system are listed below, with their international number and notation, their space groups in name and example crystals. (All these point groups are also associated with some space groups not in the rhombohedral lattice system.)[2][1][3]

# Point group Examples Space group
Class Intl Schoenflies Orbifold Coxeter
143-146 Pyramidal
rhombohedral tetartohedral
3 C3 33 [3]+ carlinite, jarosite P3, P31, P32, R3
147-148 Rhombohedral
rhombohedral tetartohedral
3 S6 3x [2+,6+] dolomite, ilmenite P3, R3
149-155 trapezohedral 32 D3 223 [2,3]+ abhurite, quartz, cinnabar P312, P321, P3112, P3121, P3212, P3221, R32
156-161 Ditrigonal Pyramidal
rhombohedral hemimorphic
3m C3v *33 [3] schorl, cerite, tourmaline, alunite, lithium tantalate P3m1, P31m, P3c1, P31c, R3m, R3c
162-167 Hexagonal Scalenohedral
rhombohedral holohedral
3m D3d 2*3 [2+,3] antimony, hematite, corundum, calcite P31m, P31c, P3m1, P3c1, R3m, R3c,