Archimedean Duals (Laves Lattices)
Laves lattices are the duals to the Archimedean lattices. Drawings from. See also Uniform Tilings.
| Lattice | z | Site Percolation Threshold | Bond Percolation Threshold | |
|---|---|---|---|---|
| Cairo pentagonal
D(32,4,3,4)=(2/3)(53)+(1/3)(54) |
3,4 | 3⅓ | 0.650184 | pcbond=1-pcbond(32,4,3,4)
0.58586256(54) |
| D(33,42)=(1/3)(54)+(2/3)(53) | 3,4 | 3⅓ | 0.647084 | pcbond=1-Pcbond(33,42)
0.58035808(57) |
| D(34,6)=(1/5)(46)+(4/5)(43) | 3,6 | 3 3/5 | 0.639447 | pcbond=1-pcbond(34,6 )
0.56569378(50) |
| dice, rhombille tiling
D(3,6,3,6)=(1/3)(46)+(2/3)(43) |
3,6 | 4 | 0.5851(4), 0.585040 | pcbond=1-pcbond(3,6,3,6 )
0.475595021(5), 0.47559500(8), 0.47559483(90), 0.475594(7) |
| ruby dual
D(3,4,6,4)=(1/6)(46)+(2/6)(43)+(3/6)(44) |
3,4,6 | 4 | 0.582410 | pcbond=1-pcbond(3,4,6,4 )
0.47516741(47) |
| bisected hexagon, cross dual
D(4,6,12)= (1/6)(312)+(2/6)(36)+(1/2)(34) |
4,6,12 | 6 | 1/2 | pcbond=1-pcbond(4,6,12)
0.30626616(28) |
| asanoha (hemp leaf)
D(3, 122)=(2/3)(33)+(1/3)(312) |
3,12 | 6 | 1/2 | pcbond=1-pcbond(3, 122)
=0.25957804(20), 0.25957918(90), 0.25957922(8) |
| union jack, tetrakis square tiling
D(4,82 )=(1/2)(34)+(1/2)(38) |
4,8 | 6 | 1/2 | pcbond=1-pcbond(4,82 )
0.23219767(37) |
Site bond percolation (both thresholds apply simultaneously to one system).
| Lattice | z | Site Percolation Threshold | Bond Percolation Threshold | |
|---|---|---|---|---|
| square | 4 | 4 | 0.615185(15) | 0.95 |
| 0.667280(15) | 0.85 | |||
| 0.732100(15) | 0.75 | |||
| 0.75 | 0.726195(15) | |||
| 0.815560(15) | 0.65 | |||
| 0.85 | 0.615810(30) | |||
| 0.95 | 0.533620(15) |
* For more values, see An Investigation of site-bond percolation
Read more about this topic: Percolation Threshold