# Rhombohedral crystal system: Wikis

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

# Encyclopedia

(Redirected to Trigonal crystal system article)

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

An example of the rhombohedral crystals, dolomite

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; $\alpha=\beta= \gamma \neq 90^\circ$. 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

Rhombohedral lattice cell

The seven space groups associated with the rhombohedral lattice system are listed below, with their international number and notation, 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

An example of the trigonal crystals, quartz
Hexagonal lattice cell

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 $\overline{3}2/m$ D3d calcite, corundum, hematite Ditrigonal Pyramidal 3m C3v tourmaline, alunite Rhombohedral $\overline{3}$ S6 dolomite, ilmenite Trapezohedral 32 D3 quartz, cinnabar Pyramidal 3 C3 jarosite

## References

1. ^ a b Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 78 - 89, ISBN 0-471-80580-7
2. ^ 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

]]

In crystallography, the rhombohedral (or trigonal) crystal system is one of the seven lattice point groups, named after the two-dimensional rhombus. A crystal 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; $\alpha, \beta, \gamma \neq 90^\circ$. In some classification schemes, the rhombohedral system is grouped into a larger hexagonal system.

There exists only one rhombohedral Bravais lattice.

## List of particulars

The point groups which fall under this crystal system are listed below, followed by their representations in international notation (Hermann-Mauguin notation) and Schoenflies notation, and example crystals.

 name international Schoenflies examples rhombohedral holohedral $\overline\left\{3\right\}m$ D3d calcite, corundum, hematite rhombohedral hemimorphic $3m$ C3v tourmaline, alunite rhombohedral tetartohedral $\overline\left\{3\right\}$ S6 dolomite, ilmenite trapezohedral $32$ D3 quartz, cinnabar rhombohedral tetartohedral $3$ C3 none verified