FIG. 5: Site percolation on the 3-12 lattice. FIG. 4: Site percolation on the (1 × 1) : (2 × 2) kagome-type subnet lattice. FIG. 3: Site percolation on the kagome lattice. Wu [9] obtained its critical frontier under a homogeneity assumption. The critical point in the case of q = 2 computed from (6) is exact. Wu [9] also used (6) to compute Potts thresholds for the 3-12 and the ( $^{m}$× m ) : ( $^{n}$× n ) kagome-type subnet lattices for $^{m,n}$≤ 4 for which the exact thresholds are not known. In addition, Wu deduced the known exact threshold of site percolation on the 3-12 lattice by considering the Potts model on the (2 × 2) : (2 × 2) kagome-type lattice as shown in Fig. 5. In this case the homogeneity assumption turns out to give the exactly known critical frontier. 5 ( q $^{2}$A + 3 qB + C )( q $^{2}$A ′ + 3 qB ′ + C $^{′}$) − 3( qB + C )( qB ′ + C $^{′}$) − ( $^{q}$− 2) CC ′ = 0 , (6)