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

International Tables for Crystallography (2006). Vol. C, ch. 9.1, p. 747

Table 9.1.1.1 

E. Kocha and W. Fischera

aInstitut 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

TypekSymmetryParametersDistance dDensity
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