Table of crystal point groups

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An all-in-one table/cheatsheet for point groups.

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Above photo by Meiying Ng on Unsplash.

Symbols: The first line is the Schönflies symbol. The second is the full international (Hermann-Mauguin) symbol. The abbreviated international symbol is provided on the next line, if any. If it's a second type point group, the decomposition is provided on the last line. The point group with the highest symmetry is highlighted with a gray background.

Projection Diagrams: Show rotation axis and mirror planes. Also show how an arbitrary point transforms and handedness change. See http://pd.chem.ucl.ac.uk/pdnn/symm2/pntgrp1.htm.

Credits: The content is based on the Group Theory textbook by Xinzhen Li and
another textbook by M.S. Dresselhaus et al. The stereographic projections are taken from http://pd.chem.ucl.ac.uk, which are created by Dr. J. K. Cockcroft, Prof. P. Barnes, Dr. M. P. Attfield, and others.

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