# List of 230 3D symmetry space groups

### This page presents the list of the 230 3D symmetry space groups with characteristics, and also, if applicable, derivatives of the space group. The table is a help for the input in the ABINIT code. You may see either the definition of the table entries (present page) or the full table.

SPGROUP | SPGAXOR | SPGORIG | BRVLTT | INTERNATIONAL | SCHOENFLIES | ORDER

This list of symmetry groups is part of the on-line help of the ABINIT code. Besides classical crystallographic information, it provides the values of certain symmetry-related variables used in the input file of the ABINIT code.

The table entries are as follows

- SPGROUP = "SPace GROUP number", as it is found in the International Tables of Crystallography, 1986 edition.
- SPGAXOR = "SPace Group AXis ORientation", the orientation of the unit cell axis. The allowed values are:

- Trigonal groups :

- 1 represents the hexagonal axes
- 2 represents the rhombohedral axes

- Orthorhombic groups:

- 1 abc -> abc
- 2 abc -> cab
- 3 abc -> bca
- 4 abc -> acb
- 5 abc -> bac
- 6 abc -> cba

- Monoclinic : 3 or 9 possibilities depending on the space group

- SPGORIG = "SPace Group ORIGin", the position of the origin in the unit cell. The allowed values are 1 and 2. they correspond to the actual choices in the International Tables of Crystallography, 1986 edition.
- BRVLTT = "BRaVais LaTTice", the type of Bravais lattice. The allowed values are:

- 1 = Primitive with no associated translations
- 2 = Inner centered with (a/2 + b/2 + c/2) associated translation
- 3 = Face centered with (a/2 + b/2; b/2 + c/2; c/2 + a/2) associated translations
- 4 = C - centered with (a/2 + b/2) associated translation
- 5 = A - centered with (b/2 + c/2) associated translation
- 6 = B - centered with (c/2 + a/2) associated translation
- 7 = Rhombohedral lattice

- INTERNATIONAL = the INTERNATIONAL notation of the space group
- SCHOENFLIES = the equivalent SCHOENFLIES notation of the space group
- MULTIPLICITY (x y z) = the maximum multiplicity, after applying Bravais lattice translations, corresponding to a general position (x y z)

Access the full table

This page has been created by Razvan Caracas.
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