International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 4.6, p. 618   | 1 | 2 |

Table 4.6.3.2 

W. Steurera* and T. Haibacha

aLaboratory of Crystallography, Department of Materials, ETH Hönggerberg, HCI G 511, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich, Switzerland
Correspondence e-mail:  walter.steurer@mat.ethz.ch

Table 4.6.3.2| top | pdf |
3D point groups of order k describing the diffraction symmetry and corresponding 6D decagonal space groups with reflection conditions (see Levitov & Rhyner, 1988[link]; Rokhsar et al., 1988[link])

3D point groupk5D space groupReflection condition
[\displaystyle{{2 \over m}}\bar{3}\bar{5}] 120 [P\displaystyle{{2 \over m}}\bar{3}\bar{5}] No condition
[P\displaystyle{{2 \over n}}\bar{3}\bar{5}] [h_{1}h_{2}\overline{h_{1}h_{2}}h_{5}h_{6}]: [h_{5} - h_{6} = 2n]
[I\displaystyle{{2 \over m}}\bar{3}\bar{5}] [h_{1}h_{2}h_{3}h_{4}h_{5}h_{6}]: [{\textstyle\sum_{i = 1}^{6}} h_{i} = 2n]
[F\displaystyle{{2 \over m}}\bar{3}\bar{5}] [h_{1}h_{2}h_{3}h_{4}h_{5}h_{6}]: [{\textstyle\sum_{i \neq j = 1}^{6}} h_{i} + h_{j} = 2n]
[F\displaystyle{{2 \over n}}\bar{3}\bar{5}] [h_{1}h_{2}h_{3}h_{4}h_{5}h_{6}]: [{\textstyle\sum_{i \neq j = 1}^{6}} h_{i} + h_{j} = 2n]
[h_{1}h_{2}\overline{h_{1}h_{2}}h_{5}h_{6}]: [h_{5} - h_{6} = 4n]
235 60 P235 No condition
[P235_{1}] [h_{1}h_{2}h_{2}h_{2}h_{2}h_{2}]: [h_{1} = 5n]
I235 [h_{1}h_{2}h_{3}h_{4}h_{5}h_{6}]: [{\textstyle\sum_{i = 1}^{6}} h_{i} = 2n]
[I235_{1}] [h_{1}h_{2}h_{3}h_{4}h_{5}h_{6}]: [{\textstyle\sum_{i = 1}^{6}} h_{i} = 2n]
  [h_{1}h_{2}h_{2}h_{2}h_{2}h_{2}]: [h_{1} + 5h_{2} = 10n]
F235 [h_{1}h_{2}h_{3}h_{4}h_{5}h_{6}]: [{\textstyle\sum_{i \neq j = 1}^{6}} h_{i} + h_{j} = 2n]
[F235_{1}] [h_{1}h_{2}h_{3}h_{4}h_{5}h_{6}]: [{\textstyle\sum_{i \neq j = 1}^{6}} h_{i} + h_{j} = 2n]
  [h_{1}h_{2}h_{2}h_{2}h_{2}h_{2}]: [h_{1} + 5h_{2} = 10n]