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.

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)