Tables for
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2015). Vol. A, ch. 1.4, pp. 43-44

Section Introduction

H. Wondratscheke Introduction

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The Hermann–Mauguin symbols, abbreviated as HM symbols in the following sections, were proposed by Hermann (1928[link], 1931[link]) and Mauguin (1931[link]), and introduced to the Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935[link]) according to the decision of the corresponding Programme Committee (Ewald, 1930[link]). There are different kinds of HM symbols of a space group. One distinguishes short HM symbols, full HM symbols and extended HM symbols. The full HM symbols will be the basis of this description. They form the most transparent kind of HM symbols and their use will minimize confusion, especially for those who are new to crystallography.

As the name suggests, the short HM symbols are mostly shortened versions of the full HM symbols: some symmetry information of the full HM symbols is omitted such that these symbols are more convenient in daily use. The full HM symbol can be reconstructed from the short symbol. In the extended HM symbols the symmetry of the space group is listed in a more complete fashion (cf. Section 1.5.4[link] ). They are rarely used in crystallographic practice.

In the next section general features of the HM symbols will be discussed. Thereafter, the HM symbols for each crystal system will be presented in a separate section, because the appearance of the HM symbols depends strongly on the crystal system to which the space group belongs.


Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935). Erster Band, Gruppentheoretische Tafeln, edited by C. Hermann. Berlin: Gebrüder Borntraeger.
Ewald, P. P. (1930). Tagung des erweiterten Tabellenkomitees in Zürich, 28. - 31. Juli 1930. Z. Kristallogr. 75, 159–160.
Hermann, C. (1928). Zur systematischen Strukturtheorie. I. Eine neue Raumgruppensymbolik. Z. Kristallogr. 68, 257–287.
Hermann, C. (1931). Bemerkung zu der vor­stehenden Arbeit von Ch. Mauguin. Z. Kristallogr. 76, 559–561.
Mauguin, M. (1931). Sur le symbolisme des groupes de répétition ou de symétrie des assemblages cristallins. Z. Kristallogr. 76, 542–558.

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