OK  27k = 18k + 18 + 3*|S cap C|  (so |S cap C| = 3k - 6 = 9(m^2-1))
OK  |S| = 4k*|S cap C|/4 = 9k(m^2-1) = (n^2-3)(n^2-9)/3, n = 3m
OK  |Q| = 12k = 4(n^2-3)
OK  vertex multiplicity 3k = n^2 - 3
OK  H(C_n) = -4(n^4 - 3n^2)/(n^4 + 27)
OK  C~.Z = 9k + 9 + 9(m^2-1) = 36m^2 - 9
OK  12k = 36m^2 - 12
OK  ell = 12(k(k+1)/2 + k) + |S| = 6k(k+3) + 9k(m^2-1)
    ell(m=1) = 60  ell(m=2) = 1221
OK  colength (k^2+3k)/2 = (k+1)(k+2)/2 - 1
OK  N = (t+3)L - (k+2)sum E_v - sum E_q - 2 sum E_s : L
OK    E_v coefficient
OK    E_q coefficient
OK    E_s coefficient
OK  decomposition: L
OK  decomposition: E_v
OK  decomposition: E_q
OK  decomposition: E_s
    b(m=2) = 7/2 (>= 7/2 for m >= 2);  b(m=1) = -1
OK  t >= 18m^2 - 9 <=> a >= 0 (6k - 3 = 18m^2 - 9)
OK  N.C~ = 3t - 45m^2 + 9
OK  N.C~ at t = 18m^2 - 9 equals 9m^2 - 18
OK  N.Et_v = (k+2) - k*1 = 2
OK  4|S| = 12k(k-2)
OK  N^2 at t+3 = 6k equals 12(k-4)(k+1)
    12(k-4)(k+1) at m=2: 1008
OK  D.Et_v = -( k*(-1) - k*(-1) ) = 0
OK  (tL - Z - K_Y).Et_v = 1 - k
OK  adjunction for Et_v: Et_v^2 + K.Et_v = (-1-k) + (k-1) = -2
OK  m = 1: N.C~ at t = 11 equals -3
OK  2(18m^2 - 8) = 36m^2 - 16
OK  N.L = 6k at t = 6k-3
OK  N.Z = 18k^2 + 24k
OK  (18k^2+24k)/(6k) = 3k + 4
OK  2(3k+4) - (6k-2) = 10
    (6k-2)/(3k+4) at m=2: 64/37

ALL IDENTITIES OK
