# Crystal system

systemlattice systemcrystallographic point groupsCrystal arrangementscrystal classcrystal familiescrystal systemsBravais lawcrystalcrystal classes
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.wikipedia
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### Hexagonal crystal family

Trigonalhexagonalrhombohedral
Crystal systems, crystal families and lattice systems are similar but slightly different, and there is widespread confusion between them: in particular the trigonal crystal system is often confused with the rhombohedral lattice system, and the term "crystal system" is sometimes used to mean "lattice system" or "crystal family".
In crystallography, the hexagonal crystal family is one of the 6 crystal families, which includes 2 crystal systems (hexagonal and trigonal) and 2 lattice systems (hexagonal and rhombohedral).

### Bravais lattice

crystal latticelatticeBravais lattices
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.
In two-dimensional space, there are 5 Bravais lattices, grouped into four crystal families.

### Space group

crystallographic groupspace groupsList of the 230 crystallographic 3D space groups
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. A lattice system is a class of lattices with the same set of lattice point groups, which are subgroups of the arithmetic crystal classes.
The space groups in three dimensions are made from combinations of the 32 crystallographic point groups with the 14 Bravais lattices, each of the latter belonging to one of 7 lattice systems.

### Crystal

crystallinecrystalscrystalline solid
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.
These are grouped into 7 crystal systems, such as cubic crystal system (where the crystals may form cubes or rectangular boxes, such as Halite (mineral) shown at right) or hexagonal crystal system (where the crystals may form hexagons, such as ordinary water ice).

### Crystallography

crystallographercrystallographiccrystallographically
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. In geometry and crystallography, a Bravais lattice is a category of translative symmetry groups (also known as lattices) in three directions.

### Triclinic crystal system

triclinicpinacoidtriclinic crystals
In crystallography, the triclinic (or anorthic) crystal system is one of the 7 crystal systems.

### Monoclinic crystal system

monoclinicmonoclinic systemmonoclinic crystal structure
In crystallography, the monoclinic crystal system is one of the 7 crystal systems.

### Orthorhombic crystal system

orthorhombicorthorombicorthorhombic system
In crystallography, the orthorhombic crystal system is one of the 7 crystal systems.

### Cubic crystal system

cubicisometricface-centered cubic
In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube.

### Tetragonal crystal system

tetragonaltetragonal systembody-centered tetragonal
In crystallography, the tetragonal crystal system is one of the 7 crystal systems.

### Rotational symmetry

axis of symmetryaxisymmetricaxis
The notation for n-fold symmetry is C n or simply "n".

### Polar point group

polar
Groups containing a polar axis are called polar.

### Crystal structure

unit celllatticecrystal lattice
The crystal structures of chiral biological molecules (such as protein structures) can only occur in the 65 enantiomorphic space groups (biological molecules are usually chiral).
They are similar to, but not quite the same as the seven crystal systems.

### Pyroelectricity

pyroelectricPyroelectric effectPyroelectric crystal
Some geometrical or physical property is different at the two ends of this axis: for example, there might develop a dielectric polarization as in pyroelectric crystals.
All crystal structures belong to one of thirty-two crystal classes based on the number of rotational axes and reflection planes they possess that leave the crystal structure unchanged (point groups).

### Point groups in three dimensions

Rotation groupbinary polyhedral grouppoint group
A lattice system is a class of lattices with the same set of lattice point groups, which are subgroups of the arithmetic crystal classes.

### Auguste Bravais

A. BravaisAuguste Bravais (1811–1863)
This was corrected to 14 by A. Bravais in 1848.
Auguste Bravais (23 August 1811, Annonay, Ardèche – 30 March 1863, Le Chesnay, France) was a French physicist known for his work in crystallography, the conception of Bravais lattices, and the formulation of Bravais law.

### Moritz Ludwig Frankenheim

The Bravais lattices were studied by Moritz Ludwig Frankenheim in 1842, who found that there were 15 Bravais lattices.
By assigning symmetry elements to the crystal systems defined previously by Weiss and Friedrich Mohs (1773-1839), Frankenheim was able, for the first time, to define 32 point groups (crystal classes) and to classify them into four crystal systems (the regular one, the fourfold, the twofold and the sixfold).

### Lattice (group)

latticelatticeslattice point
In geometry and crystallography, a Bravais lattice is a category of translative symmetry groups (also known as lattices) in three directions.

### Point group

point groupssymmetryRosette groups
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.

### Reflection symmetry

reflectionplane of symmetryreflectional symmetry

### Polarization density

polarizationelectric polarizationbound charge
Some geometrical or physical property is different at the two ends of this axis: for example, there might develop a dielectric polarization as in pyroelectric crystals.

### Protein

proteinsproteinaceousstructural proteins
The crystal structures of chiral biological molecules (such as protein structures) can only occur in the 65 enantiomorphic space groups (biological molecules are usually chiral).

### Chirality (chemistry)

chiralchiralityoptical isomer
The crystal structures of chiral biological molecules (such as protein structures) can only occur in the 65 enantiomorphic space groups (biological molecules are usually chiral).

### Cyclic group

cyclicinfinite cyclic groupinfinite cyclic

### Prism (geometry)

prismprismsprismatic