a point group: the closure of the generators its Hermann-Mauguin symbol names, written in given axes

Syntax

pg = symmetry('m-3m')

By its international symbol.

pg = symmetry('D2')

By its Schoenflies symbol or an alias.

pg = symmetry(spaceId=225)

The point group of a space group.

pg = symmetry(pointId=45)

By its number in symmetry.pointGroups.

pg = symmetry('2', abg=[90*degree, 100*degree, 90*degree])

The monoclinic setting from the lattice angles.

pg = symmetry(rotation.byAxisAngle(zvector, 90*degree))

The group the elements generate.

Description

A group says nothing about where it acts: whether it describes a crystal or a specimen, and in which coordinate system, is the business of the frame carrying it, crystalFrame or specimenFrame, which builds its group from the same symbol. The elements are built from the symbol in the order of its generators, as orthogonal transforms, proper rotations and rotoinversions; nothing refers to an element by its position.

A symbol of a monoclinic group, ‘2’, ‘m’ or ‘2/m’, names no unique axis; with the lattice angles abg the unique axis is the one whose angle is not 90 degree, as MATLAB.

Input

name str, the Hermann-Mauguin or Schoenflies symbol, a lattice name or an alias such as ‘orthotropic’; or rotation or orthogonalTransform, elements that generate the group; or a symmetry to copy; the triclinic group ‘1’ when omitted
axes vector3d or an array (3, 3), the axes a, b, c the elements are written along; x, y, z when omitted

Keywords

keyword default description
pointId None the number of the group in symmetry.pointGroups, 1 to 47
laueId None the number of a Laue class, 1 to 11
spaceId None the number of a space group, 1 to 230, which gives its point group
abg None the lattice angles alpha, beta, gamma in radians, which choose the unique axis of a monoclinic group

Output

pg symmetry, with pg.pointGroup its symbol, pg.rot its elements, pg.id its number

See also

crystalFrame, specimenFrame, symmetry.fundamentalSector, symmetry.fundamentalRegion, CrystalSymmetries

MATLAB’s symmetry.symmetry

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/symmetry.symmetry_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX 
@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.