Spacegroup Data Explorer

This website explores the crystallographic space-group and point-group datasets generated for httk. The data files used by the site are the current JSON-LD wrapped outputs in data-generators/data, copied into static/data.

Deep linking spacegroup data

Individual pages can be linked directly by several stable, site-relative URL schemes (prepend the site base URL):

• /hall/<hall entry>/ — the canonical page for a specific Hall setting, e.g. /hall/p_1/ or /hall/-c_2a_2ac/. The Hall entry is the Hall symbol written in lower case with spaces replaced by underscores.
• /itn/<IT number>/ — the standard (ITA reference) setting of a space-group number, e.g. /itn/68/, /itn/227/.
• /nc/<n:c>/ — a specific conventional setting identified by its International Tables setting code n:c, e.g. /nc/68:1/, /nc/68:1ba-c/, /nc/146:H/.
• /hm/<HM entry>/ — a specific conventional setting identified by its HM entry, written with spaces removed and "/" replaced by ":", e.g. /hm/Ccca:1/, /hm/C2:m11/, /hm/P-1/.

The /itn/, /nc/ and /hm/ links redirect to the corresponding /hall/ page. Because the three equivalent #68 setting pairs share a single page, both conventional labels of a pair (both n:c codes and both HM entries) link to that same page.

Things good to know about space groups

• There are 230 distinct three-dimensional space-group types. They are commonly identified by the sequence number in which they appear in the International Tables for Crystallography (IT), 1−230.
• Different axis choices, origin choices, and cell choices of the space-group types are called "settings". There are many different representations identifying the space groups and their settings. The most well-known are:
  • Hermann–Mauguin (HM) symbols of which there are several variants (see below).
  • Hall symbols: represents a minimal set of symmetry operations for the space group.
• Specifically, a set of 530 "conventional spacegroup settings" are present in the IT tables. However, of these actually only 527 are symmetrically unique. Three pairs of conventional settings, all in spacegroup #68, are equivalent (and, hence, share the same Hall symbol):
  • C_c_c_a:1 (#68:1) and C_c_c_b:1 (#68:1ba-c) -- Hall symbol: C 2 2 -1ac
  • A_b_a_a:1 (#68:1cab) and A_c_a_a:1 (#68:1-cba) -- Hall symbol: A 2 2 -1ab
  • B_b_c_b:1 (#68:1bca) and B_b_a_b: (#68:1a-cb) -- Hall symbol: B 2 2 -1ab
  The httk data tables therefore contains only 527 space group entries (one for each unique space group and setting). However, in some contexts the distinction between these equivalent settings matter, e.g., when discussing the mapping of Wyckoff positions in a transformation from one setting to another; in those cases we have 530 items usually keyed on the HM entry (see below).
• Variants of the HM symbols
  • Short:Referenced in IT vol A.
  • Full:Referenced in IT vol A.
  • Extended:Referenced in IT vol A. Multiline representation that is rarely used.
  • Entry:The list of all 530 conventional settings in IT table vol B, A1.4.2.7 includes a column titled "HM entry" which is the same as the full HM symbol, but where the older glide-plane letters are used, rather than the newer "e" notation (see below), and a disambiguation suffix is added if needed to distinguish between the 530 conventional space group settings.
  • Universal: The well-known [Computational Crystallography Toolbox (cctbx)](https://cctbx.github.io) defines a "universal" varity with a (somewhat different) disambiguating suffix.
• The IT HM symbols were changed in the Fourth Edition of the IT tables (IT 1995) to replace the glide plane symbol: "For the five space groups Aem2 (39), Aea2 (41), Cmce (64), Cmme (67) and Ccce (68), the ‘new’ space-group symbols, containing the symbol ‘e’ for the ‘double’ glide plane, are given for all settings. These symbols were first introduced in the Fourth Edition of this volume (IT 1995); cf. Foreword to the Fourth Edition. For further explanations, see Section 1.3.2, Note (x) and the space-group diagrams". These older symbols are included as aliases in these tables.
• Some Hall symbols also differ starting with the IT 2001 edition, with one of the primary changes being dropping the lattice symbol "S".
• Of the 230 space group types, there are 11 pairs that only differ by chirality: these are:
  • P 4₁ - (#76) and P 4₃ - (#78)
  • P 4₁ 2 2 - (#91) and P 4₃ 2 2 - (#95)
  • P 4₁ 2₁ 2 - (#92) and P 4₃ 2₁ 2 - (#96)
  • P 3₁ - (#144) and P 3₂ - (#145)
  • P 3₁ 1 2 - (#151) and P 3₂ 1 2 - (#153)
  • P 3₁ 2 1 - (#152) and P 3₂ 2 1 - (#154)
  • P 6₁ - (#169) and P 6₅ - (#170)
  • P 6₂ - (#171) and P 6₄ - (#172)
  • P 6₁ 2 2 - (#178) and P 6₅ 2 2 - (#179)
  • P 6₂ 2 2 - (#180) and P 6₄ 2 2 - (#181)
  • P 4₁ 3 2 - (#213) and P 4₃ 3 2 - (#212)