International Tables for Crystallography (2015). Vol. A, ch. 1.5, pp. 75-105

Chapter 1.5. Transformations of coordinate systems

Chapter index

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