Approximate Formulas For Thresholds of Archimedean Lattices
| Lattice | z | Site Percolation Threshold | Bond Percolation Threshold |
|---|---|---|---|
| (3, 122 ) | 3 | ||
| (4, 6, 12) | 3 | ||
| (4, 82) | 3 | 0.676835..., 4p3 + 3p4 - 6 p5- 2 p6 = 1 | |
| honeycomb (63) | 3 | ||
| kagome (3, 6, 3, 6) | 4 | 0.524430..., 3p2 + 6p3 - 12 p4+ 6 p5 - p6 = 1 | |
| (3, 4, 6, 4) | 4 | ||
| square (44) | 4 | 1/2 (exact) | |
| (34,6 ) | 5 | 0.434371..., 12p3 + 36p4 -21 p5- 327 p6 + 69p7 + 2532p8 - 6533 p9
+ 8256 p10 - 6255p11 + 2951p12 - 837 p13+ 126 p14 - 7p15= 1 |
|
| snub square, puzzle (32, 4, 3, 4 ) | 5 | ||
| (33, 42) | 5 | ||
| triangular (36) | 6 | 1/2 (exact) |
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