Table 9.1.1.1

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. 9.1, p. 747

E. Koch^a and W. Fischer^a

^a Institut für Mineralogie, Petrologie und Kristallographie, Universität Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany

Table 9.1.1.1 | top | pdf |
Types of circle packings in the plane

Type	k	Symmetry			Parameters	Distance d	Density
3⁶	6	p6mm	1(a)	0, 0		a	0.9069
3²434	5	p4gm	4(c)	$[x, x+{{1}\over{2}}]$	$[x = {{1}\over{4}}\sqrt3 - {{1}\over{4}}]$	$[{{1}\over{2}} ( \sqrt6 - \sqrt2 )a]$	0.8418
3³4²	5	c2mm	4(d)	x, 0	$[x = 1 - {{1}\over{2}}\sqrt3 ; \, b/a = 2 - \sqrt3]$	b	0.8418
3⁴6	5	p6	6(d)	x, y	$[x = {{3}\over{7}}; \, y = {{1}\over{7}}]$	$[{{1}\over{7}} \sqrt7 a]$	0.7773
4⁴	4	p4mm	1(a)	0, 0		a	0.7854
3464	4	p6mm	6(e)	$[x, \bar x ]$	$[x = {{1}\over{2}} - {{1}\over{6}} \sqrt3 ]$	$[{{1}\over{2}} ( \sqrt3 - 1) a]$	0.7290
3636	4	p6mm	3(c)	$[ {{1}\over{2}},0]$		$[ {{1}\over{2}} a]$	0.6802
6³	3	p6mm	2(b)	$[ {{1}\over{3}}, {{2}\over{3}}]$		$[ {{1}\over{3}} \sqrt3 a]$	0.6046
48²	3	p4mm	4(d)	x, 0	$[x = 1 - {{1}\over{2}}\sqrt2 ]$	$[(\sqrt2-1)a]$	0.5390
46.12	3	p6mm	12(f)	x, y	$[x = {{1}\over{6}}\sqrt3 + {{1}\over{6}}; \, y = {{1}\over{6}} \sqrt3 - {{1}\over{6}}]$	$[ ({{1}\over{2}} - {{1}\over{6}} \sqrt3)a]$	0.4860
3.12²	3	p6mm	6(c)	$[x,\bar x ]$	$[x = 1 - {{1}\over{3}}\sqrt3 ]$	$[(2-\sqrt3)a]$	0.3907