Table 4.6.3.1

Steurer, W.; Haibach, T.

doi:10.1107/97809553602060000568

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

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International Tables for Crystallography (2006). Vol. B. ch. 4.6, p. 507 | 1 | 2 |

Table 4.6.3.1

W. Steurer^a ^* and T. Haibach^a

^aLaboratory of Crystallography, Swiss Federal Institute of Technology, CH-8092 Zurich, Switzerland
Correspondence e-mail: w.steurer@kristall.erdw.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)

3D point group	k	5D space group	Reflection 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
		$[\displaystyle{P{10 \over m} {2 \over c} {2 \over c}}]$	$[h_{1}h_{2}h_{2}h_{1}h_{5}: h_{5} = 2n]$
		$[\displaystyle{P{10 \over m} {2 \over c} {2 \over c}}]$	$[h_{1}h_{2}\overline{h_{2}}\overline{h_{1}}h_{5}: h_{5} = 2n]$
		$[\displaystyle{P{10_{5} \over m} {2 \over m} {2 \over c}}]$	$[h_{1}h_{2}\overline{h_{2}}\overline{h_{1}}h_{5}: h_{5} = 2n]$
		$[\displaystyle{P{10_{5} \over m} {2 \over c} {2 \over m}}]$	$[h_{1}h_{2}h_{2}h_{1}h_{5}: h_{5} = 2n]$
$[\displaystyle{{10 \over m}}]$	20	$[\displaystyle{P{10 \over m}}]$	No condition
$[\displaystyle{{10 \over m}}]$	20	$[\displaystyle{P{10_{5} \over m}}]$	$[0000h_{5}: h_{5} = 2n]$
1022	20	P1022	No condition
1022	20	$[P10_{j}22]$	$[0000h_{5}: jh_{5} = 10n]$
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
		$[P\overline{10}2c]$	$[h_{1}h_{2}\overline{h_{2}}\overline{h_{1}}h_{5}: h_{5} = 2n]$
10	10	P10	No condition
10	10	$[P10_{j}]$	$[0000h_{5}: jh_{5} = 10n]$