Table of crystal point groups

Header: symmetry

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

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

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, which are created by Dr. J. K. Cockcroft, Prof. P. Barnes, Dr. M. P. Attfield, and others.

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Low resolution table of crystal point groups

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