Rhombohedral crystal system

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An example of trigonal rhombohedral crystals, dolomite Dolomite Dolomite is a carbonate mineral composed of calcium magnesium carbonate CaMg2. The term is also used to describe the sedimentary carbonate rock dolostone.... |
An example of trigonal crystals, quartz Quartz Quartz is the second-most-abundant mineral in the Earth's continental crust, after feldspar. It is made up of a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall formula SiO2. There are many different varieties of quartz,... |

In crystallography

Crystallography

Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...

, the

**trigonal crystal system**is one of the seven crystal system

Crystal system

In crystallography, the terms crystal system, crystal family, and lattice system each refer to one of several classes of space groups, lattices, point groups, or crystals...

s, 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

Quartz

Quartz is the second-most-abundant mineral in the Earth's continental crust, after feldspar. It is made up of a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall formula SiO2. There are many different varieties of 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 group

Point group

In geometry, a point group is a group of geometric symmetries that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O...

s 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

Hexagonal crystal system

In crystallography, the hexagonal crystal system is one of the 7 crystal systems, the hexagonal lattice system is one of the 7 lattice systems, and the hexagonal crystal family is one of the 6 crystal families...

and grouped into a larger hexagonal family.

## Rhombohedral lattice system

A lattice system is described by three basis vectors. In the rhombohedral system, the crystal is described by vectors of equal lengthLength

In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

, no two of which are orthogonal. The

**rhombohedral system**can be thought of as the cubic system stretched along a body diagonal

Diagonal

A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greek διαγώνιος , from dia- and gonia ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a...

.

*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.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.)

# | Point group | Examples | Space group | ||||
---|---|---|---|---|---|---|---|

Class | Intl Hermann-Mauguin notation Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups. It is named after the German crystallographer Carl Hermann and the French mineralogist Charles-Victor Mauguin... |
Schoenflies Schoenflies notation The Schoenflies notation or Schönflies notation, named after the German mathematician Arthur Moritz Schoenflies, is one of two conventions commonly used to describe Point groups. This notation is used in spectroscopy. The other convention is the Hermann–Mauguin notation, also known as the... |
Orbifold | Coxeter Coxeter notation In geometry, Coxeter notation is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group. It uses a bracketed notation, with modifiers to indicate certain subgroups. The notation is named after H. S. M... |
|||

143-146 | Pyramidal rhombohedral tetartohedral |
3 | C_{3} |
33 | [3^{+}] |
carlinite, jarosite Jarosite Jarosite is a basic hydrous sulfate of potassium and iron with a chemical formula of KFe3+362. This sulfate mineral is formed in ore deposits by the oxidation of iron sulfides... |
P3, P3_{1}, P3_{2}, R3 |

147-148 | Rhombohedral rhombohedral tetartohedral |
S_{6} |
3x | [2^{+},6^{+}] |
dolomite Dolomite Dolomite is a carbonate mineral composed of calcium magnesium carbonate CaMg2. The term is also used to describe the sedimentary carbonate rock dolostone.... , ilmenite Ilmenite Ilmenite is a weakly magnetic titanium-iron oxide mineral which is iron-black or steel-gray. It is a crystalline iron titanium oxide . It crystallizes in the trigonal system, and it has the same crystal structure as corundum and hematite.... |
P, R | |

149-155 | trapezohedral | 32 | D_{3} |
223 | [2,3]^{+} |
abhurite Abhurite Abhurite is a mineral of tin, oxygen, hydrogen, and chlorine with the formula Sn3O2Cl2. It is named after Sharm Abhur, a cove of the Red Sea. Its Mohs scale rating is 2.-External links:**... , quartz Quartz Quartz is the second-most-abundant mineral in the Earth's continental crust, after feldspar. It is made up of a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall formula SiO2. There are many different varieties of quartz,... , cinnabar Cinnabar Cinnabar or cinnabarite , is the common ore of mercury.-Word origin:The name comes from κινναβαρι , a Greek word most likely applied by Theophrastus to several distinct substances... |
P312, P321, P3_{1}12, P3_{1}21, P3_{2}12, P3_{2}21, R32 |

156-161 | Ditrigonal Pyramidal rhombohedral hemimorphic |
3m | C_{3v} |
*33 | [3] | schorl, cerite Cerite Cerite is a complex silicate mineral group containing cerium, formula 963. The cerium and lanthanum content varies with the Ce rich species and the La rich species... , tourmaline Tourmaline Tourmaline is a crystal boron silicate mineral compounded with elements such as aluminium, iron, magnesium, sodium, lithium, or potassium. Tourmaline is classified as a semi-precious stone and the gem comes in a wide variety of colors... , alunite Alunite Alunite is a sulfate mineral that was first observed in the 15th century in Monti della Tolfa, north of Rome, where it was mined for the manufacture of alum. First called aluminilite by J.C. Delamétherie in 1797, this name was contracted by François Beudant in 1824 to alunite.Distinct crystals of... |
P3m1, P31m, P3c1, P31c, R3m, R3c |

162-167 | Hexagonal Scalenohedral rhombohedral holohedral |
m | D_{3d} |
2*3 | [2^{+},3] |
antimony Antimony Antimony is a toxic chemical element with the symbol Sb and an atomic number of 51. A lustrous grey metalloid, it is found in nature mainly as the sulfide mineral stibnite... , hematite Hematite Hematite, also spelled as haematite, is the mineral form of iron oxide , one of several iron oxides. Hematite crystallizes in the rhombohedral system, and it has the same crystal structure as ilmenite and corundum... , corundum Corundum Corundum is a crystalline form of aluminium oxide with traces of iron, titanium and chromium. It is a rock-forming mineral. It is one of the naturally clear transparent materials, but can have different colors when impurities are present. Transparent specimens are used as gems, called ruby if red... , calcite Calcite Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate . The other polymorphs are the minerals aragonite and vaterite. Aragonite will change to calcite at 380-470°C, and vaterite is even less stable.-Properties:... |
P1m, P1c, Pm1, Pc1, Rm, Rc, |