International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.5, p. 830

Table 3.5.2.2 

E. Koch,a W. Fischera and U. Müllerb

Table 3.5.2.2| top | pdf |
Euclidean normalizers of the triclinic space groups

Basis vectors of the Euclidean normalizers ([{{\bf a}}_{c}, {{\bf b}}_{c}, {{\bf c}}_{c}] refer to the possibly centred conventional unit cell for the respective Bravais lattice): [P1{:}\ \varepsilon {{\bf a}}_{c}, \varepsilon {{\bf b}}_{c}, \varepsilon {{\bf c}}_{c}]; [P\bar{1}{:}\ {1\over 2}{{\bf a}}_{ c}, {1\over 2}{{\bf b}}_{c}, {1\over 2}{{\bf c}}_{c}].

Bravais typeEuclidean normalizer [{\cal N}\!_{\cal E}({\cal G})] of
P1 (1)[P\bar{1}] (2)
aP [P^{3}\bar{1}] [P\bar{1}]
mP [P^{3}2/m] [P2/m]
mA [P^{3}2/m] [A2/m]
oP [P^{3}mmm] Pmmm
oC [P^{3}mmm] Cmmm
oF [P^{3}mmm] Fmmm
oI [P^{3}mmm] Immm
tP [P^{3}4/mmm] [P4/mmm]
tI [P^{3}4/mmm] [I4/mmm]
hP [P^{3}6/mmm] [P6/mmm]
hR [P^{3}\bar{3}m1] [R\bar{3}m]
cP [P^{3}m\bar{3}m] [Pm\bar{3}m]
cF [P^{3}m\bar{3}m] [Fm\bar{3}m]
cI [P^{3}m\bar{3}m] [Im\bar{3}m]