Hermann–Mauguin notation
notation to represent symmetry in point groups, plane groups and space groups
In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups. 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). This notation is sometimes called international notation, because it was adopted as standard by the International Tables For Crystallography since their first edition in 1935.
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.
Point groups
Rotation axes are denoted by a number n – 1, 2, 3, 4, 5, 6, 7, 8, ... (angle of rotation φ = 360°/n). For improper rotations, Hermann–Mauguin symbols show rotoinversion axes, unlike Schoenflies and Shubnikov notations, that shows rotation-reflection axes. The rotoinversion axes are represented by the corresponding number with a macron, n – 1, 2, 3, 4, 5, 6, 7, 8, ... . 2 is equivalent to a mirror plane and usually notated as m. The direction of the mirror plane is defined as the direction perpendicular to it (the direction of the 2 axis).
Begin with the source’s own compact description: “Hermann–Mauguin notation” is notation to represent symmetry in point groups, plane groups and space groups. The dossier treats that line as a proposition to test through Hermann, Mauguin and notation, not as a finished interpretation.
Why this record matters
The phrase “notation to represent symmetry in point groups, plane groups and space groups” supplies a clear boundary for inquiry. It also exposes the unanswered questions: who defined that boundary, when it became stable and which sources sit outside it.
The citation trail is more important than the brevity of the summary: it shows where individual claims can be examined in context. The source revision retrieved here is dated May 27, 2026. The linked authority identifier is Q903232. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1928, 1931 and 1935.
A concise general-reference account can conceal disagreements about scope, terminology or the weight assigned to individual sources. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Hermann–Mauguin notation”, its source revision and the description used here.
- Expand the search: follow Hermann–Mauguin notation primary sources, Hermann–Mauguin notation archive and Hermann research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Hermann–Mauguin notation”?
- Which cited source is closest to the event, object or claim?
- What terminology or title could unlock a more precise catalogue search?
Search terms from this dossier
This entry incorporates text from “Hermann–Mauguin notation” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.