International Tables for Crystallography (2015). Vol. A, ch. 1.4, pp. 42-73
https://doi.org/10.1107/97809553602060000922

Chapter 1.4. Space groups and their descriptions

Chapter index

additional symmetry element 1.4.2.4
additional symmetry operation 1.4.2.4
affine normalizer 1.4.4.3, 1.4.4.3
arithmetic crystal class 1.4.1.6, 1.4.1.3
basis
conventional 1.4.1.3.1
primitive 1.4.1.4.2
basis vectors 1.4.1.3.1
Bieberbach groups 1.4.4.2
centred lattice 1.4.1.4.2
centring vector 1.4.1.4.2
characteristic orbit 1.4.4.4
composition series 1.4.3
computer programs
space-group symbols for 1.4.1.1
conventional crystallographic basis 1.4.1.3.1
coordinates and coordinate triplets 1.4.2.3, 1.4.4.2
coset decomposition 1.4.2.3, 1.4.2.6
coset representatives 1.4.5.1, 1.4.5.2
crystal class 1.4.3.1
cubic space groups
Hermann–Mauguin symbols for 1.4.1.4.8
cyclic groups 1.4.1.3.1
dihedral groups 1.4.1.3.1
eigensymmetry 1.4.2.5
eigensymmetry group 1.4.4.4
element set 1.4.1.4.2, 1.4.2.4
Euclidean normalizer 1.4.4.3
explicit space-group symbols 1.4.1.1
extended Hermann–Mauguin space-group symbols 1.4.1.4.1
extended Hermann–Mauguin symbols 1.4.1.4.2
extraordinary orbit 1.4.4.4
fixed-point-free space groups 1.4.4.2
full Hermann–Mauguin space-group symbols 1.4.1.4.1
general position 1.4.4.2
interpretation in terms of symmetry operations 1.4.2.3
general-position diagram 1.4.2.5
generation of a space group 1.4.3, 1.4.3.2
generators 1.4.3.1
geometric crystal class 1.4.1.3, 1.4.1.3
geometric element 1.4.1.3.1, 1.4.2.4
glide reflection 1.4.2.1, 1.4.2.5
symbol for, in Hermann–Mauguin plane-group symbols 1.4.1.5
Hall symbols 1.4.1.1
Hermann–Mauguin plane-group symbols 1.4.1.2
Hermann–Mauguin space-group symbols 1.4.1.1, 1.4.1.3
Hermann–Mauguin symbols
constituents of 1.4.1.4.2
conventional short 1.4.1.4.2
extended 1.4.1.4.2
for plane groups 1.4.1.5
for space groups 1.4.1.4
short 1.4.1.4.2
hexagonal crystal system 1.4.1.5
hexagonal space groups
Hermann–Mauguin symbols for 1.4.1.4.7.2
indicator 1.4.1.4.5
intrinsic translation part of a symmetry operation 1.4.2.4
inversion 1.4.2.1
inversion centre 1.4.2.5
Jones' faithful representation symbol 1.4.2.2
lattice
centred 1.4.1.4.2
primitive 1.4.1.4.2
layer group 1.4.5.1, 1.4.5.2
location part of a symmetry operation 1.4.2.4
monoclinic axis 1.4.1.4.4
monoclinic space groups
Hermann–Mauguin symbols for 1.4.1.4.4
multiplicity 1.4.2.3, 1.4.4.2
non-characteristic orbit 1.4.2.5, 1.4.4.4, 1.4.4.4
normalizer
Euclidean 1.4.4.3
oblique crystal system 1.4.1.5
orbit 1.4.4.1
characteristic 1.4.4.4
extraordinary 1.4.4.4
non-characteristic 1.4.2.5, 1.4.4.4, 1.4.4.4
oriented site-symmetry symbol 1.4.4.2
orthorhombic space groups
Hermann–Mauguin symbols for 1.4.1.4.5
settings 1.4.1.4.5
penetration line 1.4.5.2
plane groups 1.4.1.1, 1.4.5.3
Hermann–Mauguin symbols for 1.4.1.5, 1.4.1.2
point-group types 1.4.1.3
primitive basis 1.4.1.4.2
primitive lattice 1.4.1.4.2
projections 1.4.1.5, 1.4.5, 1.4.5.3
projection–slice theorem 1.4.5.1
rational linear section 1.4.5.2
rational planar section 1.4.5.2
rational section 1.4.5.1
rectangular crystal system 1.4.1.5
reflection (mirror reflection) 1.4.2.1
reflection conditions 1.4.4.2
special 1.4.4.4
representative symmetry directions 1.4.1.4.2, 1.4.1.4.2, 1.4.1.1, 1.4.1.2
rhombohedral space groups
Hermann–Mauguin symbols for 1.4.1.4.7.3
rod group 1.4.5.1, 1.4.5.2
rotation 1.4.2.1
rotoinversion 1.4.2.1
scanning group 1.4.5.3
Schoenflies symbols 1.4.1.3, 1.4.1.3
for space groups 1.4.1.3.2
screw rotation 1.4.2.1, 1.4.2.5
section plane 1.4.5.2
sections 1.4.1.5, 1.4.5, 1.4.5.2
rational 1.4.5.1
rational linear 1.4.5.2
rational planar 1.4.5.2
short Hermann–Mauguin space-group symbols 1.4.1.4.1
short Hermann–Mauguin symbols 1.4.1.4.2
conventional 1.4.1.4.2
side-preserving operation 1.4.5.2
side-reversing operation 1.4.5.2
simplest symmetry-operation rule 1.4.1.4.2, 1.4.1.4.5
site symmetry 1.4.4.2
site-symmetry group 1.4.4.1, 1.4.4.2
space-group numbers 1.4.1.2
space groups 1.4.1.1
diagrams of 1.4.2.5
fixed-point-free 1.4.4.2
generation of 1.4.3, 1.4.3.2
Hermann–Mauguin symbols for 1.4.1.1, 1.4.1.3
space-group symbols
extended Hermann–Mauguin symbols 1.4.1.4.1
full Hermann–Mauguin symbols 1.4.1.4.1
Hermann–Mauguin symbols 1.4.1.4
Schoenflies symbols 1.4.1.3.2
short Hermann–Mauguin symbols 1.4.1.4.1
space-group types
sequence of 1.4.1.6
special position 1.4.4.2
special reflection conditions 1.4.4.4
square crystal system 1.4.1.5
subgroups
translation subgroup 1.4.2.3, 1.4.2.6, 1.4.5.1, 1.4.5.2
subperiodic groups 1.4.5.1
symbols
explicit space-group symbols 1.4.1.1
extended Hermann–Mauguin space-group symbols 1.4.1.4.1
for symmetry operations 1.4.2.1
full Hermann–Mauguin space-group symbols 1.4.1.4.1
Hall symbols 1.4.1.1
Hermann–Mauguin plane-group symbols 1.4.1.2
Hermann–Mauguin space-group symbols 1.4.1.4, 1.4.1.1, 1.4.1.3
Jones' faithful representation symbol 1.4.2.2
oriented site-symmetry symbols 1.4.4.2
Schoenflies symbols 1.4.1.3, 1.4.1.3.2, 1.4.1.3
short Hermann–Mauguin space-group symbols 1.4.1.4.1
symmetry directions 1.4.1.4.2
symmetry element
additional 1.4.2.4
symmetry-element diagrams 1.4.2.5
symmetry operation
additional 1.4.2.4
intrinsic translation part 1.4.2.4
location part 1.4.2.4
type of 1.4.2.4
symmetry operations
relationship to general position 1.4.2.3
Seitz symbols for 1.4.2.2
symbols for 1.4.2.1
systematic absences 1.4.4.4
tetragonal space groups
Hermann–Mauguin symbols for 1.4.1.4.6
translation 1.4.2.1
translation subgroup 1.4.2.3, 1.4.2.6, 1.4.5.1, 1.4.5.2
triclinic space groups
Hermann–Mauguin symbols for 1.4.1.4.3
trigonal space groups
Hermann–Mauguin symbols for 1.4.1.4.7.1
unique monoclinic axis 1.4.1.4.4
wallpaper groups 1.4.1.5, 1.4.5.3
Wyckoff letter 1.4.4.2
Wyckoff positions 1.4.4.2, 1.4.4.2
Wyckoff set 1.4.4.3, 1.4.4.3