Hermann–Mauguin notation

H-M symbolH–M SymbolHermann-Mauguin notationH-M groupHermann–MauguinInternational notationHerman Mauguin symbolHermann- Mauguin notationHermann-MauguinHermann-Mauguin symbol
In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups.wikipedia
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Carl Hermann

It is named after the German crystallographer Carl Hermann (who introduced it in 1928) and the French mineralogist Charles-Victor Mauguin (who modified it in 1931).
With Charles-Victor Mauguin, he invented an international standard notation for crystallographic groups known as the Hermann–Mauguin notation or International notation.

Schoenflies notation

Schönflies notationSchön.Schönflies
The Hermann–Mauguin notation, compared with the Schoenflies notation, is preferred in crystallography because it can easily be used to include translational symmetry elements, and it specifies the directions of the symmetry axes.
The naming of full space groups usually follows another common convention, the Hermann–Mauguin notation, also known as the international notation.

Space group

crystallographic groupspace groupsList of the 230 crystallographic 3D space groups
In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups. The symbol of a space group is defined by combining the uppercase letter describing the lattice type with symbols specifying the symmetry elements.

Symmetry element

rotational symmetrysymmetry elements
In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups.

Triclinic crystal system

triclinicpinacoidtriclinic crystals
These are the crystallographic point groups 1 and (triclinic crystal system), 2, m, and 2⁄m (monoclinic), and 222, 2⁄m2⁄m2⁄m, and mm2 (orthorhombic).
The triclinic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number, orbifold, type, and space groups are listed in the table below.

Charles-Victor Mauguin

Charles Mauguin
It is named after the German crystallographer Carl Hermann (who introduced it in 1928) and the French mineralogist Charles-Victor Mauguin (who modified it in 1931).
French professor of mineralogy Charles-Victor Mauguin (19 September 1878 – 25 April 1958) was inventor (with Carl Hermann) of an international standard notation for crystallographic groups known as the Hermann–Mauguin notation or International notation.

Improper rotation

rotoreflectionproper rotationrotoinversion
For improper rotations, Hermann–Mauguin symbols show rotoinversion axes, unlike Schoenflies and Shubnikov notations, where the preference is given to rotation-reflection axes.

Orthorhombic crystal system

orthorhombicorthorombicorthorhombic system
These are the crystallographic point groups 1 and (triclinic crystal system), 2, m, and 2⁄m (monoclinic), and 222, 2⁄m2⁄m2⁄m, and mm2 (orthorhombic).
The orthorhombic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number, orbifold notation, type, and space groups are listed in the table below.

Cubic crystal system

cubicisometricface-centered cubic
The isometric crystal system class names, point groups (in Schönflies notation, Hermann–Mauguin notation, orbifold, and Coxeter notation), type, examples, International Tables for Crystallography space group number, and space groups are listed in the table below.

Monoclinic crystal system

monoclinicmonoclinic systemmonoclinic crystal structure
These are the crystallographic point groups 1 and (triclinic crystal system), 2, m, and 2⁄m (monoclinic), and 222, 2⁄m2⁄m2⁄m, and mm2 (orthorhombic).
It lists the International Tables for Crystallography space group numbers, followed by the crystal class name, its point group in Schoenflies notation, Hermann–Mauguin (international) notation, orbifold notation, and Coxeter notation, type descriptors, mineral examples, and the notation for the space groups.

Macron (diacritic)

macronīŪ
The rotoinversion axes are represented by the corresponding number with a macron, —,,,,,,, ... . is equivalent to a mirror plane and usually notated as m.
It is also used in Hermann–Mauguin notation.

Hexagonal crystal family

Trigonalhexagonalrhombohedral
The point groups (crystal classes) in this crystal system are listed below, followed by their representations in Hermann–Mauguin or international notation and Schoenflies notation, and mineral examples, if they exist.

Crystallographic point group

crystal classcrystallographic point groupspoint group
These are the crystallographic point groups 1 and (triclinic crystal system), 2, m, and 2⁄m (monoclinic), and 222, 2⁄m2⁄m2⁄m, and mm2 (orthorhombic).
An abbreviated form of the Hermann–Mauguin notation commonly used for space groups also serves to describe crystallographic point groups.

Diamond

diamondsdiamond miningindustrial diamond
The d glide is often called the diamond glide plane as it features in the diamond structure.

Geometry

geometricgeometricalgeometries
In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups.

Point group

point groupssymmetryRosette groups
In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups.

Crystallography

crystallographercrystallographiccrystallographically
The Hermann–Mauguin notation, compared with the Schoenflies notation, is preferred in crystallography because it can easily be used to include translational symmetry elements, and it specifies the directions of the symmetry axes.

Wallpaper group

wallpaper groupswallpaper patternplane group
In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups.

Crystal structure

unit celllatticecrystal lattice
The first letter is either lowercase p or c to represent primitive or centered unit cells.

Glide reflection

glide symmetrygliding reflectionglide plane
The presence of mirror planes are denoted m, while glide reflections are denoted g.

Bravais lattice

crystal latticelatticeBravais lattices
The symbol of a space group is defined by combining the uppercase letter describing the lattice type with symbols specifying the symmetry elements.

Screw axis

screw displacementscrew axesscrew operation
The screw axis is noted by a number, n, where the angle of rotation is 360°⁄n.

Chirality (mathematics)

chiralenantiomorphchirality
There are 4 enantiomorphic pairs of axes: (3 1 — 3 2 ), (4 1 — 4 3 ), (6 1 — 6 5 ), and (6 2 — 6 4 ).

Glide plane

glide planes
Glide planes are noted by a, b, or c depending on which axis the glide is along.