polynomial equations determining the bond percolation thresholds p$_{c}$ under the homogeneity assumption (6) for ( $^{n}$× n ) : ( $^{n}$× n ) subnet lattices in Table VI are as follows: 18 q v$_{c}$ (H) v$_{c}$ (N) c (T) c (N) X$_{h}$ (T) X$_{h}$ (N) 0 . 5 1.287715536704650 1.2877116(2) -0.445833945 -0.4458340(1) 0.082757037 0.0827569(1) 1 . 0 1.669262339202358 1.6692593(3) 0 0 0.104166667 0.10417(1) 1 . 5 1.941284616762751 1.9412832(5) 0.288024142 0.288024(1) 0.116778423 0.11678(1) 2 . 0 2.160721132019555 2.160721132(1) 0.5 0.500000(1) 1/8 0.1250000(1) 2 . 5 2.348099505779181 2.3481001(2) 0.66584083 0.66585(1) 0.130338138 0.13034(1) 3 . 0 2.513467694176093 2.5134684(2) 4/5 0.800(1) 2/15 0.1333(1) 3 . 5 2.662592230189568 2.662594(3) 0.910294591 0.911(1) 0.133771753 0.134(1) 4 . 0 2.799129506399588 2.799132(5) 1 0.999(1) 1/8 0.13(1) TABLE V: Critical properties of the Potts model on the (4 × 4) : (4 × 4) kagome lattice. (H = Homogeneity Assumption, N = Numerical, T = Theoretical universality prediction.) $^{1}$− 3 p 2 − 6 p 3 + 12 p 4 − 6 p 5 + p 6 = 0 , ( n = 1) , (32) $^{1}$− 3 p 4 − 18 p 5 − 39 p 6 + 30 p 7 + 273 p 8 + 264 p 9 − 1785 p 10 − 126 p 11 + 8232 p 12 − 162326 p 13 + 16359 p 14 − 9948 p 15 + 3708 p 16 − 786 p 17 + 73 p 18 = 0 , ( n = 2) , (33) 1 − 3 p 6 − 36 p 7 − 186 p 8 − 372 p 9 + 447 p 10 + 3558 p 11 + 4711 p 12 − 5274 p 13 − 30771 p 14 − 110816 p 15 + 69828 p 16 + 1309302 p 17 − 242760 p 18 − 10117626 p 19 + 9190737 p 20 + 53446600 p 21 − 137597577 p 22 − 15101358 p 23 + 714425889 p 24 − 1897059306 p 25 + 2985201585 p 26 − 3337272356 p 27 + 2817156177 p 28 − 1840940730 p 29 + 938230487 p 30 − 371179194 p 31 + 112125462 p 32 − 25052124 p 33 + 3909120 p 34 − 380880 p 35 + 17464 p 36 = 0 , ( n = 3) (34)