Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 2.2, p. 217


C. Giacovazzoa*

aDipartimento Geomineralogico, Campus Universitario, 70125 Bari, Italy, and Institute of Crystallography, Via G. Amendola, 122/O, 70125 Bari, Italy
Correspondence e-mail:

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Allowed origin translations, seminvariant moduli and phases for centrosymmetric primitive space groups

 H–K group
[(h, k, l){\underline P}(2, 2, 2)][(h + k, l){\underline P}(2, 2)][(l){\underline P}(2)][(h + k + l){\underline P}(2)]
Space group [P\bar{1}] Pmna [\displaystyle P {4\over m}] [\displaystyle P {4\over n} mm] [\displaystyle P\bar{3}] [R\bar{3}]
[\displaystyle P {2\over m}] Pcca [\displaystyle P {4_{2}\over m}] [\displaystyle P {4\over n}cc] [\displaystyle P \bar{3}1m] [R \bar{3}m]
[\displaystyle P {2_{1}\over m}] Pbam [\displaystyle P {4\over n}] [\displaystyle P {4_{2}\over m}mc] [\displaystyle P \bar{3}1c] [R \bar{3}c]
[\displaystyle P {2\over c}] Pccn [\displaystyle P {4_{2}\over n}] [\displaystyle P {4_{2}\over m}cm] [\displaystyle P \bar{3}m1] [\displaystyle Pm \bar{3}]
[\displaystyle P {2_{1}\over c}] Pbcm [\displaystyle P {4\over m}mm] [\displaystyle P {4_{2}\over n}bc] [\displaystyle P \bar{3}c1] [\displaystyle Pn \bar{3}]
Pmmm Pnnm [\displaystyle P {4\over m}cc] [\displaystyle P {4_{2}\over n}nm] [\displaystyle P {6\over m}] [\displaystyle Pa \bar{3}]
Pnnn Pmmn [\displaystyle P {4\over n}bm] [\displaystyle P {4_{2}\over m}bc] [\displaystyle P {6_{3}\over m}] [\displaystyle Pm \bar{3}m]
Pccm Pbcn [\displaystyle P {4\over n}nc] [\displaystyle P {4_{2}\over m}nm] [\displaystyle P {6\over m}mm] [\displaystyle Pn \bar{3}n]
Pban Pbca [\displaystyle P {4\over m}bm] [\displaystyle P {4_{2}\over n}mc] [\displaystyle P {6\over m}cc] [\displaystyle Pm \bar{3}n]
Pmma Pnma [\displaystyle P {4\over m}nc] [\displaystyle P {4_{2}\over n}cm] [\displaystyle P {6_{3}\over m}cm] [\displaystyle Pn \bar{3}m]
Pnna       [\displaystyle P {6_{3}\over m}mc]  
Allowed origin translations (0, 0, 0); [(0, {1\over 2}, {1\over 2})] (0, 0, 0) (0, 0, 0) (0, 0, 0)
[({1\over 2}, 0, 0)]; [({1\over 2}, 0, {1\over 2})] [(0, 0, {1\over 2})] [(0, 0, {1\over 2})] [({1\over 2}, {1\over 2}, {1\over 2})]
[(0, {1\over 2}, 0)]; [({1\over 2}, {1\over 2}, 0)] [({1\over 2}, {1\over 2}, 0)]    
[(0, 0, {1\over 2})]; [({1\over 2}, {1\over 2}, {1\over 2})] [({1\over 2}, {1\over 2}, {1\over 2})]    
Vector [{\bf h}_{s}] seminvariantly associated with [{\bf h} = (h, k, l)] [(h, k, l)] [(h + k, l)] (l) [(h + k + l)]
Seminvariant modulus [\boldomega _{s}] (2, 2, 2) (2, 2) (2) (2)
Seminvariant phases [\varphi_{\rm eee}] [\varphi_{\rm eee}\hbox{; } \varphi_{\rm ooe}] [\varphi_{\rm eee}\hbox{; } \varphi_{\rm eoe}] [\varphi_{\rm eee}\hbox{; } \varphi_{\rm ooe}]
    [\varphi_{\rm oee}\hbox{; } \varphi_{\rm ooe}] [\varphi_{\rm oeo}\hbox{; } \varphi_{\rm eoo}]
Number of semindependent phases to be specified 3 2 1 1