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

International Tables for Crystallography (2010). Vol. B, ch. 4.6, p. 612   | 1 | 2 |

Table 4.6.3.1 

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 4.6.3.1| top | pdf |
3D point groups of order k describing the diffraction symmetry and corresponding 5D decagonal space groups with reflection conditions (see Rabson et al., 1991[link])

3D point groupk5D space groupReflection condition
[\displaystyle{{10 \over m} {2 \over m} {2 \over m}}] 40 [\displaystyle{P{10 \over m} {2 \over m} {2 \over m}}] No condition
[\displaystyle{P{10 \over m} {2 \over c} {2 \over c}}] [h_{1}h_{2}h_{2}h_{1}h_{5}]: [h_{5} = 2n]
[h_{1}h_{2}\overline{h_{2}}\overline{h_{1}}h_{5}]: [h_{5} = 2n]
[\displaystyle{P{10_{5} \over m} {2 \over m} {2 \over c}}] [h_{1}h_{2}\overline{h_{2}}\overline{h_{1}}h_{5}]: [h_{5} = 2n]
[\displaystyle{P{10_{5} \over m} {2 \over c} {2 \over m}}] [h_{1}h_{2}h_{2}h_{1}h_{5}]: [h_{5} = 2n]
[\displaystyle{{10 \over m}}] 20 [\displaystyle{P{10 \over m}}] No condition
[\displaystyle{P{10_{5} \over m}}] [0000h_{5}]: [h_{5} = 2n]
1022 20 P1022 No condition
[P10_{j}22] [0000h_{5}]: [jh_{5} = 10n]
10mm 20 P10mm No condition
P10cc [h_{1}h_{2}h_{2}h_{1}h_{5}]: [h_{5} = 2n]
  [h_{1}h_{2}\overline{h_{2}}\overline{h_{1}}h_{5}]: [h_{5} = 2n]
[P10_{5}mc] [h_{1}h_{2}\overline{h_{2}}\overline{h_{1}}h_{5}]: [h_{5} = 2n]
[P10_{5}cm] [h_{1}h_{2}h_{2}h_{1}h_{5}]: [h_{5} = 2n]
[\overline{10}m2] 20 [P\overline{10}m2] No condition
[P\overline{10}c2] [h_{1}h_{2}h_{2}h_{1}h_{5}]: [h_{5} = 2n]
[P\overline{10}2m] No condition
[P\overline{10}2c] [h_{1}h_{2}\overline{h_{2}}\overline{h_{1}}h_{5}]: [h_{5} = 2n]
[\overline{10}] 10 [P\overline{10}] No condition
10 10 P10 No condition
[P10_{j}] [0000h_{5}]: [jh_{5} = 10n]