C = 99 q $^{6}$v8 + (2871 q $^{5}$+ 29 q $^{6}$) v $^{9}$+ (36285 q $^{4}$+ 2250 q $^{5}$) v $^{10}$+ (256785 q $^{3}$+ 47886 q 4 + 765 q $^{5}$) v 11 + (1078677 q $^{2}$+ 489164 q $^{3}$+ 30525 q $^{4}$+ 135 q $^{5}$) v 12 + (2567538 q + 2747088 q $^{2}$+ 463617 q $^{3}$+ 11898 q $^{4}$+ 9 q $^{5}$) v $^{13}$+ (2723220 + 8371674 q + 3520566 q $^{2}$+ 282843 q $^{3}$+ 2919 q $^{4}$) v $^{14}$+ (11070162 + 13828185 q + 2965938 q 2 + 120355 q $^{3}$+ 420 q $^{4}$) v 15 + (22921893 + 15205050 q + 1805958 q $^{2}$+ 36504 q $^{3}$+ 27 q $^{4}$) v 16 + (31898508 + 12327042 q + 826827 q $^{2}$+ 7773 q $^{3}$) v $^{17}$+ (33199952 + 7729828 q + 287940 q 2 + 1098 q $^{3}$) v 18 + (27253662 + 3833517 q + 75627 q $^{2}$+ 90 q $^{3}$) v 19 + (18157536 + 1513779 q + 14556 q $^{2}$+ 3 q $^{3}$) v 20 + (9965342 + 473460 q + 1938 q $^{2}$) v 21 + (4531923 + 115287 q + 159 q $^{2}$) v 22 + (1706052 + 21150 q + 6 q $^{2}$) v 23 + (527795 + 2757 q ) v $^{24}$+ (132300 + 228 q ) v 25 + (26256 + 9 q ) v $^{26}$+ 3976 v $^{27}$+ 432 v $^{28}$+ 30 v 29 + v 30 (A.4) 2. Potts model on $^{n}$× n subnets with pure 3-site coupling M Subnet $^{1}$× 1: Subnet $^{2}$× 2: Subnet $^{3}$× 3: A = 1 , B = 0 , C = m. (A.5) A = q $^{3}$+ 3 qm, B = m $^{2}$, C = m $^{3}$. (A.6) A = q 7 + 6 q $^{5}$m + 15 q $^{3}$m2 + (14 q + 3 q $^{2}$) m $^{3}$+ 3 m $^{4}$, B = q $^{2}$m3 + (2 + 2 q ) m 4 + m $^{5}$, C = 3 m 5 + m $^{6}$. (A.7) m = e $^{M}$− 1 25