B. Site percolation on the 3-12 lattice The exact critical threshold for site percolation on the 3-12 lattice is known to be s$_{c}$ = √ 1 − 2 sin( π/ 18). It was first given in [39] and is shown in I to be the same as that of the (2 × 2) : (2 × 2) Potts subnet lattice with pure 3-site interactions. To calibrate our numerical approach, we have also computed s$_{c}$ using the transfer matrix approach. Our numerical determination of critical properties of site percolation is summarized in the last row in Table VII. The comparison of numerical estimates of thresholds with exact results shows agreements up to 7 decimal places, indicating our numerical estimates to be accurate to the same degree of accuracy. Our numerical determination of the conformal anomaly and magnetic scaling dimension of site percolation indicates that these models all belong to the two-dimensional q = 1 Potts model universality class. Again, the hypothesis of universality is verified. It was shown in I, and in Sec. II, that the rigorous critical frontier (4) yields the exact $^{thresholds of site percolation on (1}$×1) : ( $^{n}$×n ) kagome-type subnet lattices. The polynomial equations determining the threshold s$_{c}$ are generated by substituting expressions of A and C in (A.5) - (A.11) into (4) and setting q = 1. This yields the site percolation thresholds shown C. Exact thresholds for site percolation on the $^{(1}$× 1) : ( $^{n}$× n ) kagome-type lattice 20 Subnet s$_{c}$ (E) s$_{c}$ (N) Other sources c (T) c (N) X$_{h}$ (T) X$_{h}$ (N) $^{(1}$× $^{1) : (1}$× $^{1) 0.652703644666139 0.6527035(2) 1}$− 2 sin( π/ 18) [35] 0 0 0.1041667 0.1042(1) $^{(1}$× $^{1) : (2}$× 2) 0.707106781186548 0.7071068(2) 1 $_{/}$√$_{2 [36]}$ 0 0 0.1041667 0.10416(1) $^{(1}$× $^{1) : (3}$× 3) 0.728355596425196 0.7283555(1) 0 0 0.1041667 0.10417(1) $^{(1}$× $^{1) : (4}$× 4) 0.738348473943256 0.7383483(5) 0 0 0.1041667 0.10417(2) $^{(1}$× $^{1) : (5}$× 5) 0.743548682503071 0.7435486(3) 0 0 0.1041667 0.1042(1) $^{(1}$× $^{1) : (6}$× 6) 0.746418147634282 0.7464180(3) 0 0 0.1041667 0.10417(1) 3-12 lattice √ $^{1}$− 2 sin( π/ 18) 0.8079008(3) √ $^{1}$− 2 sin( π/ 18) [39] 0 0 0.1041667 0.10416(1) =0.807900764120 0.807904(4) [N] [39] $^{TABLE VII: Critical properties of site percolation on (1}$× 1) : ( $^{n}$× n ) kagome-type subnet lattices and the 3-12 lattice. (E = Exact result, N = Numerical, T = Theoretical universality prediction.)