Table 6.1.1.10

Maslen, E. N.; Fox, A. G.; O'Keefe, M. A.

doi:10.1107/97809553602060000600

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 6.1, p. 586

Table 6.1.1.10

E. N. Maslen,^e ^‡ A. G. Fox^b and M. A. O'Keefe^c

Table 6.1.1.10 | top | pdf |
Indices nmp allowed by the site symmetry for the functions $[H_n(z)\Phi_{mp}(\varphi)]$ ; μ, ν and j are integers such that m, n ≥ 0; (−)ⁿ implies p = − for n odd and p = + for n even

Site symmetry	Coordinate axes	Indices
1	Any	$[{\rm All}\,\,(n,m,p)]$
$[\bar1]$	Any
2	$[2\parallel x]$	$[(n,m,(-)^{n})]$
	$[2\parallel y]$	$[(n,m,(-)^{n-m})]$
	$[2\parallel z]$	$[(n,2\nu,p)]$
m	$[m\,\bot\, x]$	$[(n,m,(-)^{m})]$
	$[m\,\bot\, y]$
	$[m\,\bot\, z]$	$[(2\mu,m,p)]$
	$[2\parallel x,m\,\bot\,x]$	$[(m+2j ,m,(-)^{m})]$
	$[2\parallel y,m\,\bot\,y]$
	$[2\parallel z,m\,\bot\,z]$	$[(2\mu,2\nu,p)]$
222	$[2\parallel z,2\parallel y]$	$[(n,2\nu,(-)^n)]$
	$[2\parallel x,m\,\bot\,z]$	$[(2\mu,m+)]$
	$[2\parallel y,m\,\bot\,z]$	$[(2\mu,m,(-)^m)]$
	$[2\parallel z,m\,\bot\,y]$	$[(n,2\nu,+)]$
	$[m\,\bot\,z,m\,\bot\,y,m\,\bot\,z]$	$[(2\mu,2\nu,+)]$
4	$[4\parallel z]$	$[(n,4\nu,p)]$
$[\bar4]$	$[\bar4\parallel z]$
	$[4\parallel z,m\,\bot\,z]$	$[(2\mu,4\nu,p)]$
422	$[4\parallel z,2\parallel y]$	$[(n,4\nu,(-)^n)]$
	$[4\parallel z,m\,\bot\,y]$	$[(n,4\nu,+)]$
$[\bar42m]$	$[\bar4\parallel z,2\parallel x]$
	$[\bar4\parallel z,m\,\bot\,y]$
	$[4\parallel z,m\,\bot\,z,m\,\bot\,x]$	$[(2\mu,4\nu,+)]$
3	$[3\parallel z]$	$[(n,3\nu,p)]$
$[\bar3]$	$[\bar3\parallel z]$	$[(m+2j,3\nu,p)]$
32	$[3\parallel z,2\parallel y]$	$[(n,3\nu,(-)^{n-m})]$
	$[3\parallel z,2\parallel x]$	$[(n,3\nu,(-)^{n})]$
	$[3\parallel z,m\,\bot\,y]$	$[(n,3\nu,+)]$
	$[3\parallel z,m\,\bot\,x]$	$[(n,3\nu,(-)^m)]$
$[\bar3m]$	$[\bar3\parallel z,m\,\bot\,y]$	$[(m+2j,3\nu,+)]$
$[\bar3m]$	$[\bar3\parallel z,m\,\bot\,x]$	$[(m+2j,3\nu,(-)^m)]$
6	$[6\parallel z]$	$[(n,6\nu,p)]$
$[\bar6]$	$[\bar6\parallel z]$	$[(2\mu,3\nu,p)]$
	$[6\parallel z,m\,\bot\,z]$	$[(2\mu,6\nu,p)]$
622	$[6\parallel z,2\parallel y]$	$[(n,6\nu,(-)^n)]$
	$[6\parallel z,m\,\bot\,y]$	$[(n,6\nu,+)]$
$[\bar6m2]$	$[\bar6\parallel z,m\,\bot\,y]$	$[(2\mu,3\nu,+)]$
$[\bar6m2]$	$[\bar6\parallel z,m\,\bot\,x]$	$[(2\mu,3\nu,(-)^m)]$
	$[6\parallel z,m\,\bot\,z,m\,\bot\,y]$	$[(2\mu,6\nu,+)]$