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A more rational order for the 230 space groups.

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Title: A more rational order for the 230 space groups.
Authors: Aroyo, Mois I.1 (AUTHOR) mois.aroyo@gmail.com, Brock, Carolyn Pratt2 (AUTHOR) cpbrock@uky.edu
Source: Journal of Applied Crystallography. Jun2026, Vol. 59 Issue 3, p932-942. 11p.
Subjects: Space groups, Crystallography, College teaching, Crystal structure, Crystal symmetry, Symmetry, Symmetry groups
Abstract: The order of the space groups in International Tables for Crystallography is full of inconsistencies, all of which can be traced back to the order Schoenflies published in 1891. The many inconsistencies obscure the relationships between the space groups and therefore make teaching about them more difficult. A more rational order based on a small number of principles has been developed. The order of the crystal systems and the order of the geometric crystal classes (i.e. the point groups) are unchanged; they have been considered carefully and revised in the past. What is new is that groups within geometric crystal classes are sorted first by arithmetic crystal class (point group plus centering type of the conventional cell) and then by the number and type of symmetry elements for which the defining operations (1) have intrinsic translation parts (i.e. are screw axes or glide planes) and (2) appear in the full Hermann–Mauguin symbol of the space group. While it seems unlikely that the new ordering will replace the current order, it is recommended that it be adopted as an alternative in space‐group studies and in teaching of crystallographic symmetry. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Crystallography is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: <searchLink fieldCode="DE" term="%22Space+groups%22">Space groups</searchLink><br /><searchLink fieldCode="DE" term="%22Crystallography%22">Crystallography</searchLink><br /><searchLink fieldCode="DE" term="%22College+teaching%22">College teaching</searchLink><br /><searchLink fieldCode="DE" term="%22Crystal+structure%22">Crystal structure</searchLink><br /><searchLink fieldCode="DE" term="%22Crystal+symmetry%22">Crystal symmetry</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry%22">Symmetry</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry+groups%22">Symmetry groups</searchLink>
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  Data: The order of the space groups in International Tables for Crystallography is full of inconsistencies, all of which can be traced back to the order Schoenflies published in 1891. The many inconsistencies obscure the relationships between the space groups and therefore make teaching about them more difficult. A more rational order based on a small number of principles has been developed. The order of the crystal systems and the order of the geometric crystal classes (i.e. the point groups) are unchanged; they have been considered carefully and revised in the past. What is new is that groups within geometric crystal classes are sorted first by arithmetic crystal class (point group plus centering type of the conventional cell) and then by the number and type of symmetry elements for which the defining operations (1) have intrinsic translation parts (i.e. are screw axes or glide planes) and (2) appear in the full Hermann–Mauguin symbol of the space group. While it seems unlikely that the new ordering will replace the current order, it is recommended that it be adopted as an alternative in space‐group studies and in teaching of crystallographic symmetry. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Applied Crystallography is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1107/S1600576726002360
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 11
        StartPage: 932
    Subjects:
      – SubjectFull: Space groups
        Type: general
      – SubjectFull: Crystallography
        Type: general
      – SubjectFull: College teaching
        Type: general
      – SubjectFull: Crystal structure
        Type: general
      – SubjectFull: Crystal symmetry
        Type: general
      – SubjectFull: Symmetry
        Type: general
      – SubjectFull: Symmetry groups
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      – TitleFull: A more rational order for the 230 space groups.
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            NameFull: Brock, Carolyn Pratt
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            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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