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 triclinic crystal system is one of the 7 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. A crystal system is described by three basis vectors. In the triclinic system, the crystal

Crystal

A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

 is described by vectors of unequal length, as in the orthorhombic system. In addition, all three vectors are not mutually orthogonal.

The triclinic lattice is the least symmetric of the 14 three-dimensional Bravais lattices. It has (itself) the minimum symmetry all lattices have: points of inversion at each lattice point and at 7 more points for each lattice point: at the midpoints of the edges and the faces, and at the center points. It is the only lattice type that itself has no mirror planes.

Triclinic Crystal Classes

The triclincic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation

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...

, point groups

Crystallographic point group

In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a central point fixed while moving other directions and faces of the crystal to the positions of features of the same kind...

, International Tables for Crystallography space group number, orbifold

Orbifold

In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold is a generalization of a manifold...

, type, and space groups are listed in the table below. There are a total 2 space groups.

#	Point group					Example	Type	Space group Space group In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains.In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered distinct...
	Class	Schönflies 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...	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...	orbifold Orbifold In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold is a generalization of a manifold...	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...
1	Pedial	C1	1	11	[ ]+	Tantite Tantite Tantite is a rare tantalum oxide mineral with formula: Ta2O5. Tantite forms transparent microscopic colorless triclinic - pedial crystals with an adamantine luster. It has a Mohs hardness of 7 and a high specific gravity of 8.45. Chemical analyses show minor inclusion of niobium oxide.It was first...	enantiomorphic polar Chemical polarity In chemistry, polarity refers to a separation of electric charge leading to a molecule or its chemical groups having an electric dipole or multipole moment. Polar molecules interact through dipole–dipole intermolecular forces and hydrogen bonds. Molecular polarity is dependent on the difference in...	P1
2	Pinacoidal	Ci (= S2)		1x	[2+,2+]	Wollastonite Wollastonite Wollastonite is a calcium inosilicate mineral that may contain small amounts of iron, magnesium, and manganese substituting for calcium. It is usually white. It forms when impure limestone or dolostone is subjected to high temperature and pressure sometimes in the presence of silica-bearing fluids...	centrosymmetric	P

With each only one space group is associated. Pinacoidal is also known as triclinic normal. Pedial is also triclinic hemihedral

Mineral

Mineral

A mineral is a naturally occurring solid chemical substance formed through biogeochemical processes, having characteristic chemical composition, highly ordered atomic structure, and specific physical properties. By comparison, a rock is an aggregate of minerals and/or mineraloids and does not...

 examples include plagioclase

Plagioclase

Plagioclase is an important series of tectosilicate minerals within the feldspar family. Rather than referring to a particular mineral with a specific chemical composition, plagioclase is a solid solution series, more properly known as the plagioclase feldspar series...

, microcline

Microcline

Microcline is an important igneous rock-forming tectosilicate mineral. It is a potassium-rich alkali feldspar. Microcline typically contains minor amounts of sodium. It is common in granite and pegmatites. Microcline forms during slow cooling of orthoclase; it is more stable at lower temperatures...

, rhodonite

Rhodonite

Rhodonite is a manganese inosilicate, SiO3 and member of the pyroxenoid group of minerals, crystallizing in the triclinic system...

, turquoise

Turquoise

Turquoise is an opaque, blue-to-green mineral that is a hydrous phosphate of copper and aluminium, with the chemical formula CuAl648·4. It is rare and valuable in finer grades and has been prized as a gem and ornamental stone for thousands of years owing to its unique hue...

, wollastonite

Wollastonite

Wollastonite is a calcium inosilicate mineral that may contain small amounts of iron, magnesium, and manganese substituting for calcium. It is usually white. It forms when impure limestone or dolostone is subjected to high temperature and pressure sometimes in the presence of silica-bearing fluids...

 and amblygonite

Amblygonite

Amblygonite is a fluorophosphate mineral, AlPO4, composed of lithium, sodium, aluminium, phosphate, fluoride and hydroxide. The mineral occurs in pegmatite deposits and is easily mistaken for albite and other feldspars. Its density, cleavage and flame test for lithium are diagnostic. Amblygonite...

, all in triclinic normal (bar 1).