International Tables for Crystallography (2015). Vol. A, ch. 1.5, pp. 75-105
https://doi.org/10.1107/97809553602060000923

Chapter 1.5. Transformations of coordinate systems

Chapter index

additional symmetry elements 1.5.4.1, 1.5.4.1.3
additional symmetry operations 1.5.4.1, 1.5.4.1.3, 1.5.4.1.3, 1.5.4.1, 1.5.4.2
augmented matrix 1.5.2.4
basis 1.5.1.1
change of 1.5.1.2
dual 1.5.2.1
reciprocal 1.5.2.1
basis vectors
transformation of 1.5.1.1
C and c cell (tetragonal and hexagonal lattices) 1.5.4.3
c cell (square lattice) 1.5.4.2
cell
cell choice
monoclinic 1.5.4.4
centred cell 1.5.4.1.3, 1.5.4.2
c centred 1.5.4.2
coaxial symmetry operation 1.5.4.1.1, 1.5.4.1.2
coordinate system
transformation of u1.5.1, 1.5.1.2, 1.5.1.2, 1.5.1.3
coplanar symmetry operation 1.5.4.1.1, 1.5.4.1.2
coset 1.5.4.1.2
cubic space groups 1.5.4.4
diagrams of 1.5.4.1.3
D cell (hexagonal lattice) 1.5.3.1, 1.5.1.1
dual basis 1.5.2.1
e glide 1.5.4.3
extended Hermann–Mauguin plane-group symbols 1.5.4.3
extended Hermann–Mauguin space-group symbols 1.5.4, 1.5.4.3, 1.5.4.4
F cell (tetragonal lattice) 1.5.4.4
fixed point 1.5.4.1.1
g glide 1.5.4.3, 1.5.4.3
H and h cell (hexagonal lattice) 1.5.4.2, 1.5.4.3, 1.5.1.1
Hermann–Mauguin plane-group symbols
extended 1.5.4.3
Hermann–Mauguin space-group symbols
extended 1.5.4, 1.5.4.3, 1.5.4.4
hexagonal axes, cell and coordinate system 1.5.1.1
hexagonal plane groups 1.5.4.3
hexagonal space groups 1.5.4.4
intrinsic translation part of a symmetry operation 1.5.4.1.1, 1.5.4.1.1
location of a symmetry operation 1.5.4.1, 1.5.4.2
location part of a symmetry operation 1.5.4.1.1, 1.5.4.1.1
mapping of mappings 1.5.2.3
matrices for unit-cell (basis) transformation 1.5.1.1
metric tensor 1.5.2.2
Miller indices 1.5.2.1, 1.5.2.4
monoclinic settings and cell choices 1.5.3.1, 1.5.3.2.1, 1.5.4.3, 1.5.1.1, 1.5.4.4
monoclinic space groups 1.5.4.4
oblique plane groups 1.5.4.3
obverse setting of R cell 1.5.3.1, 1.5.1.1
origin choice 1.5.3.1, 1.5.3.2.2
origin shift 1.5.1.1
orthohexagonal C cell 1.5.4.3, 1.5.1.1
orthorhombic settings 1.5.4.3, 1.5.1.1
orthorhombic space groups 1.5.4.4
phase transitions 1.5.2.5
basic (parent) structure 1.5.2.5
derivative structure 1.5.2.5
plane groups 1.5.4.3
symbols for 1.5.4.2, 1.5.4.3
R cell (rhombohedral lattice) 1.5.3.1, 1.5.1.1
obverse 1.5.3.1
reverse 1.5.3.1
reciprocal basis 1.5.2.1
rectangular plane groups 1.5.4.3
reduced symmetry operation 1.5.4.1.1
reflection conditions
transformation of 1.5.3.2.1, 1.5.3.1
reverse setting of R cell 1.5.3.1, 1.5.1.1
rhombohedral axes, cell and coordinate system 1.5.3.1, 1.5.1.1
rhombohedral space groups 1.5.3.1, 1.5.4.1.3, 1.5.4.4
Schoenflies space-group symbols 1.5.4.4
screw rotation 1.5.4.1.3
settings 1.5.3.1, 1.5.4
monoclinic 1.5.1.1, 1.5.4.4
orthorhombic 1.5.1.1, 1.5.4.4
rhombohedral, obverse and reverse 1.5.1.1
shift vector 1.5.1.3
space groups
symbols for 1.5.4, 1.5.4.3, 1.5.4.4
transformations between different descriptions of 1.5.3
square plane groups 1.5.4.3
symbols
for plane groups 1.5.4.2, 1.5.4.3
for space groups 1.5.4.3, 1.5.4.4
symmetry element
additional 1.5.4.1, 1.5.4.1.3
symmetry operation
intrinsic translation part 1.5.4.1.1, 1.5.4.1.1
location of 1.5.4.1, 1.5.4.2
location part 1.5.4.1.1, 1.5.4.1.1
reduced 1.5.4.1.1
transformation of 1.5.2.3, 1.5.3.2.1
type of 1.5.4.1.1
tetragonal space groups 1.5.4.4
transformation of basis vectors 1.5.1.1
transformation of coordinate system u1.5.1, 1.5.1.2
contravariant quanities 1.5.2.1
covariant quantities 1.5.2.1
general 1.5.1.3
linear part 1.5.1.2
transformation of reflection conditions 1.5.3.2.1, 1.5.3.1
transformation of symmetry operations 1.5.2.3, 1.5.3.2.1
transformations between different space-group descriptions 1.5.3
translation subgroup 1.5.4.1.3
triclinic space groups 1.5.4.4
trigonal space groups 1.5.4.4
unique monoclinic axis 1.5.3.1, 1.5.3.2.1, 1.5.4.4