ribbon graph 0 sigma_0 = (0,10,23)(1,19,13)(2,18,14)(3,6,20)(4,17,16)(5,9,22)(7,12,11)(8,21,15) alpha_0 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_0 = (0,7,1,19,11,10,9,8,6,2,18,3,21,5,4,17,22)(12,23)(13)(14)(15,20)(16) Aut(G_0) = 1 edge-face adjacency matrix [1 1 1 1 1 2 2 2 1 2 2 1] [1 0 0 0 0 0 0 0 0 0 0 1] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 1 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 1 sigma_1 = (0,5,22)(1,19,13)(2,18,14)(3,6,20)(4,17,16)(7,12,11)(8,21,15)(9,23,10) alpha_1 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_1 = (0,7,1,19,11,9,8,6,2,18,3,21,10,5,4,17)(12,22,23)(13)(14)(15,20)(16) Aut(G_1) = 1 edge-face adjacency matrix [1 1 1 1 1 2 2 2 1 2 1 1] [1 0 0 0 0 0 0 0 0 0 1 1] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 1 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 2 sigma_2 = (0,20,12)(1,22,13)(2,10,23)(3,18,15)(4,17,16)(5,6,19)(7,21,8)(9,14,11) alpha_2 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_2 = (0,20,21,11,10,1,22,2,9,7,6,3,18,5,4,17,19,8)(12)(13)(14,23)(15)(16) Aut(G_2) = 1 edge-face adjacency matrix [1 1 1 1 1 2 2 2 2 2 2 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 1] [0 0 0 1 0 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 3 sigma_3 = (0,20,12)(1,8,21)(2,10,23)(3,18,15)(4,17,16)(5,6,19)(7,14,11)(9,22,13) alpha_3 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_3 = (0,20,1,22,2,7,6,3,18,5,4,17,19,11,10,9,8)(12)(13,21)(14,23)(15)(16) Aut(G_3) = 1 edge-face adjacency matrix [1 1 1 1 1 2 2 2 2 1 2 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 1] [0 0 0 1 0 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 4 sigma_4 = (0,21,12)(1,20,13)(2,8,22)(3,18,15)(4,17,16)(5,6,19)(7,14,11)(9,23,10) alpha_4 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_4 = (0,21,10,8,1,20,2,7,6,3,18,5,4,17,19,11,9)(12)(13)(14,22,23)(15)(16) Aut(G_4) = 1 edge-face adjacency matrix [1 1 1 1 1 2 2 2 2 2 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 5 sigma_5 = (0,22,12)(1,10,23)(2,20,14)(3,18,15)(4,17,16)(5,6,19)(7,8,21)(9,13,11) alpha_5 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_5 = (0,22,1,9,8,2,20,7,6,3,18,5,4,17,19,21,11,10)(12)(13,23)(14)(15)(16) Aut(G_5) = 1 edge-face adjacency matrix [1 1 1 1 1 2 2 2 2 2 2 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 1] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 6 sigma_6 = (0,23,12)(1,22,13)(2,20,14)(3,18,15)(4,17,16)(5,6,19)(7,8,21)(9,10,11) alpha_6 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_6 = (0,23,10,1,22,9,8,2,20,7,6,3,18,5,4,17,19,21,11)(12)(13)(14)(15)(16) Aut(G_6) = 1 edge-face adjacency matrix [1 1 1 1 1 2 2 2 2 2 2 2] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 7 sigma_7 = (0,7,23)(1,21,13)(2,20,14)(3,18,15)(4,17,16)(5,6,19)(8,9,22)(10,12,11) alpha_7 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_7 = (0,10,9,1,21,8,2,20,22,11,7,6,3,18,5,4,17,19)(12,23)(13)(14)(15)(16) Aut(G_7) = C2 edge-face adjacency matrix [1 1 1 1 1 2 2 2 2 2 2 1] [1 0 0 0 0 0 0 0 0 0 0 1] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 8 sigma_8 = (0,5,19)(1,8,21)(2,10,23)(3,18,15)(4,17,16)(6,14,11)(7,20,12)(9,22,13) alpha_8 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_8 = (0,20,1,22,2,6,3,18,11,10,9,8,7,5,4,17)(12,19)(13,21)(14,23)(15)(16) Aut(G_8) = C2 edge-face adjacency matrix [1 1 1 1 1 2 2 1 2 1 2 1] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 1] [0 0 0 1 0 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 9 sigma_9 = (0,5,21)(1,20,13)(2,19,14)(3,18,15)(4,17,16)(6,22,9)(7,23,10)(8,12,11) alpha_9 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_9 = (0,8,1,20,11,7,2,19,10,6,3,18,9,5,4,17)(12,21,22,23)(13)(14)(15)(16) Aut(G_9) = C4 edge-face adjacency matrix [1 1 1 1 1 2 2 2 2 1 1 1] [1 0 0 0 0 0 0 0 0 1 1 1] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 10 sigma_10 = (0,16,17)(1,7,21)(2,4,18)(3,8,22)(5,19,12)(6,20,14)(9,11,13)(10,23,15) alpha_10 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_10 = (0,19,1,11,10,8,6,4)(2,20,3,23,9,7,5,16)(12,17)(13,21)(14,18)(15,22) Aut(G_10) = D8 edge-face adjacency matrix [1 1 0 0 1 0 1 1 1 0 1 1] [0 0 1 1 1 1 0 1 1 1 0 1] [1 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] [0 0 1 0 0 0 1 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 11 sigma_11 = (0,17,12)(1,5,18)(2,4,20)(3,9,22)(6,19,13)(7,16,11)(8,21,14)(10,23,15) alpha_11 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_11 = (0,17,1,19,11,10,9,8,4,7,6,5)(2,21,3,23,16)(12)(13,18)(14,20)(15,22) Aut(G_11) = 1 edge-face adjacency matrix [1 1 0 0 1 2 1 2 1 1 1 1] [0 0 1 1 1 0 0 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 1 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 12 sigma_12 = (0,17,12)(1,5,19)(2,18,14)(3,6,20)(4,22,8)(7,16,21)(9,11,13)(10,23,15) alpha_12 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_12 = (0,17,1,11,10,4,7,5)(2,18,3,23,9,16,8,6)(12)(13,19,21)(14)(15,20,22) Aut(G_12) = C2 edge-face adjacency matrix [1 1 0 0 1 2 0 1 0 0 1 1] [0 0 1 1 1 0 2 0 1 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 1 0 1 0] -------------------------------------------------------------------------------- ribbon graph 13 sigma_13 = (0,17,12)(1,5,19)(2,18,14)(3,9,22)(4,21,6)(7,20,13)(8,16,11)(10,23,15) alpha_13 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_13 = (0,17,1,20,11,10,9,4,8,7,5)(2,18,21,3,23,16,6)(12)(13,19)(14)(15,22) Aut(G_13) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 1 2 1 1 1] [0 0 1 1 1 0 2 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 14 sigma_14 = (0,17,12)(1,5,19)(2,18,14)(3,6,21)(4,22,9)(7,20,13)(8,16,11)(10,23,15) alpha_14 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_14 = (0,17,1,20,11,10,4,8,7,5)(2,18,3,23,16,9,6)(12)(13,19)(14)(15,21,22) Aut(G_14) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 1 2 0 1 1] [0 0 1 1 1 0 2 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 15 sigma_15 = (0,17,12)(1,5,19)(2,18,14)(3,6,21)(4,8,11)(7,20,13)(9,22,15)(10,23,16) alpha_15 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_15 = (0,17,1,20,4,23,8,7,5)(2,18,3,22,16,11,10,9,6)(12)(13,19)(14)(15,21) Aut(G_15) = C2 edge-face adjacency matrix [1 1 0 0 1 2 0 1 2 0 0 1] [0 0 1 1 1 0 2 0 0 1 2 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 16 sigma_16 = (0,17,12)(1,19,13)(2,18,14)(3,9,22)(4,20,6)(5,16,11)(7,21,8)(10,23,15) alpha_16 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_16 = (0,17,11,10,9,7,1,19,8,4,5)(2,18,20,21,3,23,16,6)(12)(13)(14)(15,22) Aut(G_16) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 1 1 1 1] [0 0 1 1 1 0 2 0 1 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 17 sigma_17 = (0,17,12)(1,19,13)(2,18,14)(3,8,21)(4,20,6)(5,16,11)(7,22,9)(10,23,15) alpha_17 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_17 = (0,17,11,10,7,1,19,9,8,4,5)(2,18,20,3,23,16,6)(12)(13)(14)(15,21,22) Aut(G_17) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 1 1 1 1] [0 0 1 1 1 0 2 0 1 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 18 sigma_18 = (0,17,12)(1,19,13)(2,18,14)(3,6,20)(4,21,8)(5,16,11)(7,22,9)(10,23,15) alpha_18 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_18 = (0,17,11,10,7,1,19,9,4,5)(2,18,3,23,16,8,6)(12)(13)(14)(15,20,21,22) Aut(G_18) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 0 1 1 1] [0 0 1 1 1 0 2 0 1 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 1 1 1 0] -------------------------------------------------------------------------------- ribbon graph 19 sigma_19 = (0,17,12)(1,19,13)(2,18,14)(3,6,20)(4,10,23)(5,22,7)(8,21,15)(9,11,16) alpha_19 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_19 = (0,17,7,1,19,22,4,11,10,5)(2,18,3,21,16,23,9,8,6)(12)(13)(14)(15,20) Aut(G_19) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 0 0 2 1] [0 0 1 1 1 0 2 0 1 2 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 1 0 0 0] -------------------------------------------------------------------------------- ribbon graph 20 sigma_20 = (0,17,12)(1,19,13)(2,18,14)(3,6,20)(4,7,11)(5,16,22)(8,21,15)(9,23,10) alpha_20 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_20 = (0,17,22,23,7,1,19,4,5)(2,18,3,21,10,16,11,9,8,6)(12)(13)(14)(15,20) Aut(G_20) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 0 0 1 1] [0 0 1 1 1 0 2 0 1 2 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 1 0 0 0] -------------------------------------------------------------------------------- ribbon graph 21 sigma_21 = (0,17,12)(1,19,13)(2,18,14)(3,6,20)(4,7,21)(5,16,11)(8,9,22)(10,23,15) alpha_21 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_21 = (0,17,11,10,9,7,1,19,4,5)(2,18,3,23,16,21,8,6)(12)(13)(14)(15,20,22) Aut(G_21) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 0 1 1 1] [0 0 1 1 1 0 2 0 1 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 1 0 1 0] -------------------------------------------------------------------------------- ribbon graph 22 sigma_22 = (0,17,12)(1,19,13)(2,18,14)(3,9,22)(4,21,6)(5,20,7)(8,16,11)(10,23,15) alpha_22 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_22 = (0,17,7,1,19,20,11,10,9,4,8,5)(2,18,21,3,23,16,6)(12)(13)(14)(15,22) Aut(G_22) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 2 1 1 1] [0 0 1 1 1 0 2 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 23 sigma_23 = (0,17,12)(1,19,13)(2,18,14)(3,6,21)(4,22,9)(5,20,7)(8,16,11)(10,23,15) alpha_23 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_23 = (0,17,7,1,19,20,11,10,4,8,5)(2,18,3,23,16,9,6)(12)(13)(14)(15,21,22) Aut(G_23) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 2 0 1 1] [0 0 1 1 1 0 2 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 24 sigma_24 = (0,17,12)(1,19,13)(2,18,14)(3,20,15)(4,9,11)(5,21,7)(6,22,8)(10,23,16) alpha_24 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_24 = (0,17,7,1,19,21,4,23,9,5)(2,18,8,3,20,22,16,11,10,6)(12)(13)(14)(15) Aut(G_24) = C2 edge-face adjacency matrix [1 1 0 0 1 2 0 2 0 2 0 1] [0 0 1 1 1 0 2 0 2 0 2 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 25 sigma_25 = (0,17,12)(1,19,13)(2,18,14)(3,20,15)(4,22,6)(5,21,7)(8,11,16)(9,23,10) alpha_25 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_25 = (0,17,7,1,19,21,10,4,11,9,5)(2,18,22,23,8,3,20,16,6)(12)(13)(14)(15) Aut(G_25) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 0 2 1 1] [0 0 1 1 1 0 2 0 2 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 26 sigma_26 = (0,17,12)(1,19,13)(2,18,14)(3,20,15)(4,7,22)(5,11,10)(6,23,9)(8,21,16) alpha_26 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_26 = (0,17,10,7,1,19,4,21,23,5)(2,18,9,8,3,20,16,22,11,6)(12)(13)(14)(15) Aut(G_26) = C2 edge-face adjacency matrix [1 1 0 0 1 2 0 2 0 1 1 1] [0 0 1 1 1 0 2 0 2 1 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 27 sigma_27 = (0,17,12)(1,19,13)(2,18,14)(3,20,15)(4,7,23)(5,9,22)(6,11,10)(8,21,16) alpha_27 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_27 = (0,17,22,11,7,1,19,4,21,5)(2,18,10,9,8,3,20,16,23,6)(12)(13)(14)(15) Aut(G_27) = C2 x C2 edge-face adjacency matrix [1 1 0 0 1 2 0 2 0 1 1 1] [0 0 1 1 1 0 2 0 2 1 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 28 sigma_28 = (0,17,12)(1,19,13)(2,18,14)(3,9,22)(4,7,20)(5,16,11)(6,8,21)(10,23,15) alpha_28 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_28 = (0,17,11,10,9,8,7,1,19,4,5)(2,18,21,3,23,16,20,6)(12)(13)(14)(15,22) Aut(G_28) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 1 1 1 1] [0 0 1 1 1 0 2 0 1 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 29 sigma_29 = (0,17,12)(1,18,13)(2,7,20)(3,9,22)(4,6,19)(5,16,11)(8,21,14)(10,23,15) alpha_29 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_29 = (0,17,11,10,9,8,7,6,1,18,4,5)(2,21,3,23,16,19)(12)(13)(14,20)(15,22) Aut(G_29) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 1 1 1 1 1] [0 0 1 1 1 0 0 1 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 30 sigma_30 = (0,17,12)(1,18,13)(2,4,19)(3,9,22)(5,16,11)(6,21,8)(7,20,14)(10,23,15) alpha_30 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_30 = (0,17,11,10,9,6,1,18,8,7,4,5)(2,20,21,3,23,16)(12)(13)(14,19)(15,22) Aut(G_30) = C2 edge-face adjacency matrix [1 1 0 0 1 2 2 1 1 1 1 1] [0 0 1 1 1 0 0 0 1 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 31 sigma_31 = (0,17,12)(1,18,13)(2,4,19)(3,8,21)(5,16,11)(6,22,9)(7,20,14)(10,23,15) alpha_31 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_31 = (0,17,11,10,6,1,18,9,8,7,4,5)(2,20,3,23,16)(12)(13)(14,19)(15,21,22) Aut(G_31) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 1 1 1 1 1] [0 0 1 1 1 0 0 0 1 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 32 sigma_32 = (0,17,12)(1,18,13)(2,4,20)(3,9,22)(5,19,6)(7,16,11)(8,21,14)(10,23,15) alpha_32 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_32 = (0,17,6,1,18,19,11,10,9,8,4,7,5)(2,21,3,23,16)(12)(13)(14,20)(15,22) Aut(G_32) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 2 1 1 1 1] [0 0 1 1 1 0 0 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 33 sigma_33 = (0,17,12)(1,5,19)(2,9,22)(3,18,15)(4,8,21)(6,11,16)(7,20,13)(10,23,14) alpha_33 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_33 = (0,17,1,20,4,11,10,9,8,7,5)(2,23,6,3,18,16,21)(12)(13,19)(14,22)(15) Aut(G_33) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 1 2 1 1 1] [0 0 1 1 1 0 2 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 34 sigma_34 = (0,17,12)(1,5,19)(2,4,21)(3,18,15)(6,11,16)(7,20,13)(8,22,9)(10,23,14) alpha_34 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_34 = (0,17,1,20,9,4,11,10,8,7,5)(2,23,6,3,18,16)(12)(13,19)(14,21,22)(15) Aut(G_34) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 1 2 1 1 1] [0 0 1 1 1 0 2 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 35 sigma_35 = (0,17,12)(1,19,13)(2,9,22)(3,18,15)(4,7,20)(5,21,8)(6,11,16)(10,23,14) alpha_35 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_35 = (0,17,8,7,1,19,4,11,10,9,5)(2,23,6,3,18,16,20,21)(12)(13)(14,22)(15) Aut(G_35) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 1 1 1 1] [0 0 1 1 1 0 2 0 1 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 36 sigma_36 = (0,17,12)(1,19,13)(2,8,21)(3,18,15)(4,7,20)(5,22,9)(6,11,16)(10,23,14) alpha_36 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_36 = (0,17,9,8,7,1,19,4,11,10,5)(2,23,6,3,18,16,20)(12)(13)(14,21,22)(15) Aut(G_36) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 1 1 1 1] [0 0 1 1 1 0 2 0 1 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 37 sigma_37 = (0,17,12)(1,19,13)(2,4,20)(3,18,15)(5,22,9)(6,11,16)(7,21,8)(10,23,14) alpha_37 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_37 = (0,17,9,7,1,19,8,4,11,10,5)(2,23,6,3,18,16)(12)(13)(14,20,21,22)(15) Aut(G_37) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 1 1 1 1] [0 0 1 1 1 0 2 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 38 sigma_38 = (0,17,12)(1,19,13)(2,9,22)(3,18,15)(4,8,21)(5,20,7)(6,11,16)(10,23,14) alpha_38 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_38 = (0,17,7,1,19,20,4,11,10,9,8,5)(2,23,6,3,18,16,21)(12)(13)(14,22)(15) Aut(G_38) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 2 1 1 1] [0 0 1 1 1 0 2 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 39 sigma_39 = (0,17,12)(1,19,13)(2,4,21)(3,18,15)(5,20,7)(6,11,16)(8,22,9)(10,23,14) alpha_39 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_39 = (0,17,7,1,19,20,9,4,11,10,8,5)(2,23,6,3,18,16)(12)(13)(14,21,22)(15) Aut(G_39) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 2 2 1 1 1] [0 0 1 1 1 0 2 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 40 sigma_40 = (0,7,20)(1,17,13)(2,4,21)(3,18,15)(5,22,9)(6,19,16)(8,11,12)(10,23,14) alpha_40 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_40 = (0,11,10,5,1,17,9,4,19)(2,23,8,7,6,3,18,16)(12,20)(13)(14,21,22)(15) Aut(G_40) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 1 0 1 1 1] [0 0 1 1 1 0 2 1 1 0 0 1] [1 0 0 0 0 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 41 sigma_41 = (0,7,20)(1,17,13)(2,4,21)(3,18,15)(5,10,11)(6,19,16)(8,22,12)(9,23,14) alpha_41 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_41 = (0,22,5,1,17,11,9,4,19)(2,23,10,8,7,6,3,18,16)(12,20)(13)(14,21)(15) Aut(G_41) = C2 edge-face adjacency matrix [1 1 0 0 1 2 0 1 0 1 1 1] [0 0 1 1 1 0 2 1 1 0 1 1] [1 0 0 0 0 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 42 sigma_42 = (0,16,19)(1,17,13)(2,4,20)(3,18,15)(5,22,8)(6,11,9)(7,21,12)(10,23,14) alpha_42 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_42 = (0,21,11,10,5,1,17,8,4)(2,23,6,3,18,9,7,16)(12,19)(13)(14,20,22)(15) Aut(G_42) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 0 1 1 1 1] [0 0 1 1 1 0 2 1 0 1 0 1] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 43 sigma_43 = (0,16,19)(1,17,13)(2,4,20)(3,18,15)(5,10,11)(6,22,9)(7,21,12)(8,23,14) alpha_43 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_43 = (0,21,22,5,1,17,11,8,4)(2,23,10,6,3,18,9,7,16)(12,19)(13)(14,20)(15) Aut(G_43) = C2 edge-face adjacency matrix [1 1 0 0 1 2 0 0 1 1 1 1] [0 0 1 1 1 0 2 1 0 1 1 1] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 44 sigma_44 = (0,16,19)(1,17,13)(2,4,20)(3,18,15)(5,9,22)(6,11,10)(7,21,12)(8,23,14) alpha_44 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_44 = (0,21,5,1,17,22,11,8,4)(2,23,6,3,18,10,9,7,16)(12,19)(13)(14,20)(15) Aut(G_44) = C2 edge-face adjacency matrix [1 1 0 0 1 2 0 0 1 1 1 1] [0 0 1 1 1 0 2 1 0 1 1 1] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 45 sigma_45 = (0,17,12)(1,5,18)(2,7,20)(3,4,22)(6,19,13)(8,21,14)(9,16,11)(10,23,15) alpha_45 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_45 = (0,17,1,19,2,21,11,10,4,9,8,7,6,5)(3,23,16)(12)(13,18)(14,20)(15,22) Aut(G_45) = 1 edge-face adjacency matrix [1 1 1 0 1 2 1 2 1 2 1 1] [0 0 0 1 1 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 1 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 46 sigma_46 = (0,17,12)(1,18,13)(2,7,20)(3,4,22)(5,19,6)(8,21,14)(9,16,11)(10,23,15) alpha_46 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_46 = (0,17,6,1,18,19,2,21,11,10,4,9,8,7,5)(3,23,16)(12)(13)(14,20)(15,22) Aut(G_46) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 2 1 2 1 1] [0 0 0 1 1 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 47 sigma_47 = (0,17,12)(1,18,13)(2,20,14)(3,9,22)(4,8,21)(5,19,6)(7,16,11)(10,23,15) alpha_47 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_47 = (0,17,6,1,18,19,11,10,9,8,2,20,4,7,5)(3,23,16,21)(12)(13)(14)(15,22) Aut(G_47) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 2 2 1 1 1] [0 0 0 1 1 0 0 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 48 sigma_48 = (0,17,12)(1,18,13)(2,20,14)(3,4,21)(5,19,6)(7,16,11)(8,22,9)(10,23,15) alpha_48 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_48 = (0,17,6,1,18,19,11,10,8,2,20,9,4,7,5)(3,23,16)(12)(13)(14)(15,21,22) Aut(G_48) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 2 2 1 1 1] [0 0 0 1 1 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 49 sigma_49 = (0,17,12)(1,18,13)(2,20,14)(3,4,22)(5,19,6)(7,21,8)(9,16,11)(10,23,15) alpha_49 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_49 = (0,17,6,1,18,19,8,2,20,21,11,10,4,9,7,5)(3,23,16)(12)(13)(14)(15,22) Aut(G_49) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 2 2 2 1 1] [0 0 0 1 1 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 50 sigma_50 = (0,17,12)(1,18,13)(2,6,19)(3,9,22)(4,8,21)(5,16,11)(7,20,14)(10,23,15) alpha_50 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_50 = (0,17,11,10,9,8,7,6,1,18,2,20,4,5)(3,23,16,21)(12)(13)(14,19)(15,22) Aut(G_50) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 1 2 1 1 1] [0 0 0 1 1 0 0 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 51 sigma_51 = (0,17,12)(1,18,13)(2,6,19)(3,4,21)(5,16,11)(7,20,14)(8,22,9)(10,23,15) alpha_51 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_51 = (0,17,11,10,8,7,6,1,18,2,20,9,4,5)(3,23,16)(12)(13)(14,19)(15,21,22) Aut(G_51) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 1 2 1 1 1] [0 0 0 1 1 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 52 sigma_52 = (0,17,12)(1,18,13)(2,6,19)(3,4,21)(5,16,11)(7,20,14)(8,23,10)(9,22,15) alpha_52 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_52 = (0,17,11,8,7,6,1,18,2,20,10,9,4,5)(3,22,23,16)(12)(13)(14,19)(15,21) Aut(G_52) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 1 2 1 1 1] [0 0 0 1 1 0 0 0 0 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 53 sigma_53 = (0,17,12)(1,18,13)(2,6,19)(3,4,22)(5,21,8)(7,20,14)(9,16,11)(10,23,15) alpha_53 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_53 = (0,17,8,7,6,1,18,2,20,21,11,10,4,9,5)(3,23,16)(12)(13)(14,19)(15,22) Aut(G_53) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 1 2 2 1 1] [0 0 0 1 1 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 54 sigma_54 = (0,17,12)(1,18,13)(2,19,14)(3,9,22)(4,7,20)(5,16,11)(6,21,8)(10,23,15) alpha_54 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_54 = (0,17,11,10,9,6,1,18,8,7,2,19,4,5)(3,23,16,20,21)(12)(13)(14)(15,22) Aut(G_54) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 2 1 1 1 1] [0 0 0 1 1 0 0 0 1 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 55 sigma_55 = (0,17,12)(1,18,13)(2,19,14)(3,8,21)(4,7,20)(5,16,11)(6,22,9)(10,23,15) alpha_55 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_55 = (0,17,11,10,6,1,18,9,8,7,2,19,4,5)(3,23,16,20)(12)(13)(14)(15,21,22) Aut(G_55) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 2 1 1 1 1] [0 0 0 1 1 0 0 0 1 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 56 sigma_56 = (0,17,12)(1,18,13)(2,19,14)(3,9,22)(4,8,21)(5,16,11)(6,20,7)(10,23,15) alpha_56 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_56 = (0,17,11,10,9,8,6,1,18,7,2,19,20,4,5)(3,23,16,21)(12)(13)(14)(15,22) Aut(G_56) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 2 2 1 1 1] [0 0 0 1 1 0 0 0 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 57 sigma_57 = (0,17,12)(1,18,13)(2,19,14)(3,4,22)(5,21,8)(6,20,7)(9,16,11)(10,23,15) alpha_57 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_57 = (0,17,8,6,1,18,7,2,19,20,21,11,10,4,9,5)(3,23,16)(12)(13)(14)(15,22) Aut(G_57) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 2 2 2 1 1] [0 0 0 1 1 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 58 sigma_58 = (0,17,12)(1,5,19)(2,18,14)(3,4,22)(6,8,21)(7,20,13)(9,16,11)(10,23,15) alpha_58 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_58 = (0,17,1,20,6,2,18,21,11,10,4,9,8,7,5)(3,23,16)(12)(13,19)(14)(15,22) Aut(G_58) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 1 2 2 1 1] [0 0 0 1 1 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 59 sigma_59 = (0,17,12)(1,5,22)(2,18,14)(3,4,19)(6,13,11)(7,20,15)(8,21,16)(9,23,10) alpha_59 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_59 = (0,17,1,6,2,18,11,9,8,7,4,21,10,5)(3,20,16)(12)(13,22,23)(14)(15,19) Aut(G_59) = 1 edge-face adjacency matrix [1 1 1 0 1 2 2 1 1 2 1 1] [0 0 0 1 1 0 0 0 1 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 1 1] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 1 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 60 sigma_60 = (0,16,18)(1,7,20)(2,9,22)(3,17,15)(4,11,5)(6,19,12)(8,21,13)(10,23,14) alpha_60 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_60 = (0,19,1,21,2,23,4)(3,17,11,10,9,8,7,6,16,5)(12,18)(13,20)(14,22)(15) Aut(G_60) = 1 edge-face adjacency matrix [1 1 1 0 1 0 0 1 0 1 0 1] [0 0 0 1 1 2 1 1 1 1 1 1] [1 0 0 0 0 0 1 0 0 0 0 0] [0 1 0 0 0 0 0 0 1 0 0 0] [0 0 1 0 0 0 0 0 0 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 61 sigma_61 = (0,18,12)(1,6,19)(2,8,21)(3,17,15)(4,10,23)(5,11,16)(7,20,13)(9,22,14) alpha_61 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_61 = (0,18,1,20,2,22,4,11,10,9,8,7,6)(3,17,16,23,5)(12)(13,19)(14,21)(15) Aut(G_61) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 1 2 1 2 1] [0 0 0 1 1 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 62 sigma_62 = (0,18,12)(1,19,13)(2,8,21)(3,17,15)(4,10,23)(5,11,16)(6,20,7)(9,22,14) alpha_62 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_62 = (0,18,7,1,19,20,2,22,4,11,10,9,8,6)(3,17,16,23,5)(12)(13)(14,21)(15) Aut(G_62) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 2 1 2 1] [0 0 0 1 1 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 63 sigma_63 = (0,18,12)(1,19,13)(2,21,14)(3,17,15)(4,10,23)(5,11,16)(6,20,7)(8,22,9) alpha_63 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_63 = (0,18,7,1,19,20,9,2,21,22,4,11,10,8,6)(3,17,16,23,5)(12)(13)(14)(15) Aut(G_63) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 2 2 2 1] [0 0 0 1 1 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 64 sigma_64 = (0,18,12)(1,19,13)(2,21,14)(3,17,15)(4,22,5)(6,20,7)(8,16,11)(9,23,10) alpha_64 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_64 = (0,18,7,1,19,20,11,9,2,21,10,4,8,6)(3,17,22,23,16,5)(12)(13)(14)(15) Aut(G_64) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 2 2 1 1] [0 0 0 1 1 2 0 0 0 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 65 sigma_65 = (0,18,12)(1,19,13)(2,7,20)(3,17,15)(4,10,23)(5,11,16)(6,21,8)(9,22,14) alpha_65 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_65 = (0,18,8,7,1,19,2,22,4,11,10,9,6)(3,17,16,23,5)(12)(13)(14,20,21)(15) Aut(G_65) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 1 1 2 1] [0 0 0 1 1 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 1 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 66 sigma_66 = (0,18,12)(1,19,13)(2,7,20)(3,17,15)(4,10,23)(5,11,16)(6,22,9)(8,21,14) alpha_66 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_66 = (0,18,9,8,7,1,19,2,21,22,4,11,10,6)(3,17,16,23,5)(12)(13)(14,20)(15) Aut(G_66) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 1 2 2 1] [0 0 0 1 1 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 67 sigma_67 = (0,18,12)(1,19,13)(2,7,20)(3,17,15)(4,22,5)(6,16,11)(8,21,14)(9,23,10) alpha_67 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_67 = (0,18,11,9,8,7,1,19,2,21,10,4,6)(3,17,22,23,16,5)(12)(13)(14,20)(15) Aut(G_67) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 1 2 1 1] [0 0 0 1 1 2 0 0 0 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 68 sigma_68 = (0,18,12)(1,19,13)(2,20,14)(3,17,15)(4,10,23)(5,11,16)(6,22,9)(7,21,8) alpha_68 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_68 = (0,18,9,7,1,19,8,2,20,21,22,4,11,10,6)(3,17,16,23,5)(12)(13)(14)(15) Aut(G_68) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 2 2 2 1] [0 0 0 1 1 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 69 sigma_69 = (0,18,12)(1,19,13)(2,20,14)(3,17,15)(4,9,22)(5,11,16)(6,23,10)(7,21,8) alpha_69 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_69 = (0,18,10,9,7,1,19,8,2,20,21,4,11,6)(3,17,16,22,23,5)(12)(13)(14)(15) Aut(G_69) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 2 2 1 1] [0 0 0 1 1 2 0 0 0 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 70 sigma_70 = (0,18,12)(1,19,13)(2,20,14)(3,17,15)(4,8,21)(5,11,16)(6,23,10)(7,22,9) alpha_70 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_70 = (0,18,10,7,1,19,9,8,2,20,4,11,6)(3,17,16,21,22,23,5)(12)(13)(14)(15) Aut(G_70) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 2 1 1 1] [0 0 0 1 1 2 0 0 0 1 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 71 sigma_71 = (0,18,12)(1,6,20)(2,19,14)(3,17,15)(4,10,23)(5,11,16)(7,9,22)(8,21,13) alpha_71 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_71 = (0,18,1,21,7,2,19,22,4,11,10,9,8,6)(3,17,16,23,5)(12)(13,20)(14)(15) Aut(G_71) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 1 2 2 1] [0 0 0 1 1 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 1 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 72 sigma_72 = (0,18,12)(1,6,20)(2,19,14)(3,17,15)(4,7,22)(5,11,16)(8,21,13)(9,23,10) alpha_72 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_72 = (0,18,1,21,10,7,2,19,4,11,9,8,6)(3,17,16,22,23,5)(12)(13,20)(14)(15) Aut(G_72) = 1 edge-face adjacency matrix [1 1 1 0 1 0 2 2 1 2 1 1] [0 0 0 1 1 2 0 0 0 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 1 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 73 sigma_73 = (0,17,12)(1,5,18)(2,8,21)(3,4,20)(6,19,13)(7,22,9)(10,23,14)(11,16,15) alpha_73 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_73 = (0,17,1,19,9,8,4,11,10,7,6,5)(2,23,15,20)(3,16)(12)(13,18)(14,21,22) Aut(G_73) = 1 edge-face adjacency matrix [1 1 0 0 1 2 1 2 1 1 1 1] [0 0 1 1 0 0 0 0 1 0 0 1] [0 0 0 1 1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 1 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 74 sigma_74 = (0,17,12)(1,5,18)(2,3,20)(4,21,8)(6,19,13)(7,16,11)(9,22,14)(10,23,15) alpha_74 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_74 = (0,17,1,19,11,10,9,4,7,6,5)(2,22,15)(3,23,16,8)(12)(13,18)(14,20,21) Aut(G_74) = 1 edge-face adjacency matrix [1 1 0 0 1 2 1 2 0 1 1 1] [0 0 1 1 0 0 0 0 0 0 1 0] [0 0 0 1 1 0 0 0 1 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 1 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 1 0 0] -------------------------------------------------------------------------------- ribbon graph 75 sigma_75 = (0,17,12)(1,5,18)(2,3,20)(4,22,9)(6,19,13)(7,16,11)(8,21,14)(10,23,15) alpha_75 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_75 = (0,17,1,19,11,10,4,7,6,5)(2,21,22,15)(3,23,16,9,8)(12)(13,18)(14,20) Aut(G_75) = 1 edge-face adjacency matrix [1 1 0 0 1 2 1 2 0 0 1 1] [0 0 1 1 0 0 0 0 0 1 1 0] [0 0 0 1 1 0 0 0 1 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 1 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] -------------------------------------------------------------------------------- ribbon graph 76 sigma_76 = (0,17,12)(1,5,21)(2,3,18)(4,11,8)(6,19,14)(7,20,15)(9,16,22)(10,23,13) alpha_76 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_76 = (0,17,1,23,4,9,5)(2,19,15)(3,20,11,10,16,8,7,6)(12)(13,21,22)(14,18) Aut(G_76) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 0 0 1 0 1] [0 0 1 1 0 0 0 1 0 0 0 0] [0 0 0 1 1 0 1 1 2 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 1 0] [0 0 1 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 77 sigma_77 = (0,17,12)(1,5,21)(2,3,18)(4,10,23)(6,19,14)(7,20,15)(8,11,16)(9,22,13) alpha_77 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_77 = (0,17,1,22,4,11,10,9,5)(2,19,15)(3,20,16,23,8,7,6)(12)(13,21)(14,18) Aut(G_77) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 0 0 1 2 1] [0 0 1 1 0 0 0 1 0 0 0 0] [0 0 0 1 1 0 1 1 2 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] [0 0 1 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 78 sigma_78 = (0,17,12)(1,21,13)(2,3,18)(4,10,23)(5,22,9)(6,19,14)(7,20,15)(8,11,16) alpha_78 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_78 = (0,17,9,1,21,22,4,11,10,5)(2,19,15)(3,20,16,23,8,7,6)(12)(13)(14,18) Aut(G_78) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 0 0 2 2 1] [0 0 1 1 0 0 0 1 0 0 0 0] [0 0 0 1 1 0 1 1 2 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 79 sigma_79 = (0,17,12)(1,21,13)(2,3,18)(4,9,22)(5,23,10)(6,19,14)(7,20,15)(8,11,16) alpha_79 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_79 = (0,17,10,9,1,21,4,11,5)(2,19,15)(3,20,16,22,23,8,7,6)(12)(13)(14,18) Aut(G_79) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 0 0 2 1 1] [0 0 1 1 0 0 0 1 0 0 0 0] [0 0 0 1 1 0 1 1 2 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 80 sigma_80 = (0,17,12)(1,18,13)(2,8,21)(3,4,19)(5,22,9)(6,20,7)(10,23,14)(11,16,15) alpha_80 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_80 = (0,17,9,8,6,1,18,7,4,11,10,5)(2,23,15,19,20)(3,16)(12)(13)(14,21,22) Aut(G_80) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 1 1 1 1 1] [0 0 1 1 0 0 0 1 1 0 0 1] [0 0 0 1 1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 81 sigma_81 = (0,17,12)(1,18,13)(2,3,19)(4,20,7)(5,16,11)(6,22,9)(8,21,14)(10,23,15) alpha_81 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_81 = (0,17,11,10,6,1,18,9,8,4,5)(2,21,22,15)(3,23,16,7)(12)(13)(14,19,20) Aut(G_81) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 0 1 1 1 1] [0 0 1 1 0 0 0 0 0 1 1 0] [0 0 0 1 1 0 0 1 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 1 0 0 0] -------------------------------------------------------------------------------- ribbon graph 82 sigma_82 = (0,17,12)(1,18,13)(2,3,19)(4,21,8)(5,16,11)(6,22,9)(7,20,14)(10,23,15) alpha_82 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_82 = (0,17,11,10,6,1,18,9,4,5)(2,20,21,22,15)(3,23,16,8,7)(12)(13)(14,19) Aut(G_82) = C2 edge-face adjacency matrix [1 1 0 0 1 2 2 0 0 1 1 1] [0 0 1 1 0 0 0 0 1 1 1 0] [0 0 0 1 1 0 0 1 1 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 83 sigma_83 = (0,17,12)(1,18,13)(2,3,19)(4,6,21)(5,16,11)(7,20,14)(8,9,22)(10,23,15) alpha_83 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_83 = (0,17,11,10,9,6,1,18,4,5)(2,20,22,15)(3,23,16,21,8,7)(12)(13)(14,19) Aut(G_83) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 0 0 1 1 1] [0 0 1 1 0 0 0 0 1 0 1 0] [0 0 0 1 1 0 0 1 1 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 84 sigma_84 = (0,17,12)(1,18,13)(2,3,19)(4,6,20)(5,16,11)(7,8,21)(9,22,14)(10,23,15) alpha_84 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_84 = (0,17,11,10,9,8,6,1,18,4,5)(2,22,15)(3,23,16,20,7)(12)(13)(14,19,21) Aut(G_84) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 0 1 1 1 1] [0 0 1 1 0 0 0 0 0 0 1 0] [0 0 0 1 1 0 0 1 1 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 85 sigma_85 = (0,17,12)(1,18,13)(2,8,21)(3,7,20)(4,6,19)(5,22,9)(10,23,14)(11,16,15) alpha_85 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_85 = (0,17,9,8,7,6,1,18,4,11,10,5)(2,23,15,20)(3,16,19)(12)(13)(14,21,22) Aut(G_85) = C2 edge-face adjacency matrix [1 1 0 0 1 2 2 1 1 1 1 1] [0 0 1 1 0 0 0 0 1 0 0 1] [0 0 0 1 1 0 0 1 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 86 sigma_86 = (0,17,12)(1,18,13)(2,8,21)(3,7,20)(4,6,19)(5,16,11)(9,22,14)(10,23,15) alpha_86 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_86 = (0,17,11,10,9,8,7,6,1,18,4,5)(2,22,15,20)(3,23,16,19)(12)(13)(14,21) Aut(G_86) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 1 1 1 1 1] [0 0 1 1 0 0 0 0 1 0 1 0] [0 0 0 1 1 0 0 1 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 87 sigma_87 = (0,17,12)(1,18,13)(2,8,21)(3,4,20)(5,19,6)(7,22,9)(10,23,14)(11,16,15) alpha_87 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_87 = (0,17,6,1,18,19,9,8,4,11,10,7,5)(2,23,15,20)(3,16)(12)(13)(14,21,22) Aut(G_87) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 2 1 1 1 1] [0 0 1 1 0 0 0 0 1 0 0 1] [0 0 0 1 1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 88 sigma_88 = (0,17,12)(1,18,13)(2,3,20)(4,21,8)(5,19,6)(7,16,11)(9,22,14)(10,23,15) alpha_88 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_88 = (0,17,6,1,18,19,11,10,9,4,7,5)(2,22,15)(3,23,16,8)(12)(13)(14,20,21) Aut(G_88) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 2 0 1 1 1] [0 0 1 1 0 0 0 0 0 0 1 0] [0 0 0 1 1 0 0 0 1 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 1 0 0] -------------------------------------------------------------------------------- ribbon graph 89 sigma_89 = (0,17,12)(1,18,13)(2,3,20)(4,22,9)(5,19,6)(7,16,11)(8,21,14)(10,23,15) alpha_89 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_89 = (0,17,6,1,18,19,11,10,4,7,5)(2,21,22,15)(3,23,16,9,8)(12)(13)(14,20) Aut(G_89) = 1 edge-face adjacency matrix [1 1 0 0 1 2 2 2 0 0 1 1] [0 0 1 1 0 0 0 0 0 1 1 0] [0 0 0 1 1 0 0 0 1 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0] -------------------------------------------------------------------------------- ribbon graph 90 sigma_90 = (0,16,18)(1,8,21)(2,3,17)(4,19,5)(6,20,12)(7,22,14)(9,11,13)(10,23,15) alpha_90 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_90 = (0,20,1,11,10,7,4)(2,22,15)(3,23,9,8,6,16,5)(12,18)(13,21)(14,17,19) Aut(G_90) = C2 edge-face adjacency matrix [1 1 0 0 1 0 0 1 1 0 1 1] [0 0 1 1 0 0 0 0 0 0 1 0] [0 0 0 1 1 1 1 0 1 1 0 1] [1 0 0 0 0 0 1 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] [0 0 1 0 0 1 0 1 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 91 sigma_91 = (0,6,19)(1,8,21)(2,17,14)(3,4,11)(5,22,9)(7,20,12)(10,23,13)(15,18,16) alpha_91 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_91 = (0,20,1,23,4,18)(2,17,9,8,7,6,15,11,10,5)(3,16)(12,19)(13,21,22)(14) Aut(G_91) = 1 edge-face adjacency matrix [1 1 0 0 1 0 1 0 1 0 0 1] [0 0 1 1 0 2 1 1 1 1 1 1] [0 0 0 1 1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 1 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 92 sigma_92 = (0,18,12)(1,6,19)(2,17,14)(3,10,23)(4,8,22)(5,21,15)(7,20,13)(9,11,16) alpha_92 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_92 = (0,18,1,20,4,11,10,8,7,6)(2,17,15,23,9,5)(3,21,16,22)(12)(13,19)(14) Aut(G_92) = 1 edge-face adjacency matrix [1 1 0 0 1 0 2 1 2 0 1 1] [0 0 1 1 0 2 0 0 0 1 0 1] [0 0 0 1 1 0 0 0 0 1 1 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 93 sigma_93 = (0,18,12)(1,19,13)(2,17,14)(3,10,23)(4,8,22)(5,21,15)(6,20,7)(9,11,16) alpha_93 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_93 = (0,18,7,1,19,20,4,11,10,8,6)(2,17,15,23,9,5)(3,21,16,22)(12)(13)(14) Aut(G_93) = 1 edge-face adjacency matrix [1 1 0 0 1 0 2 2 2 0 1 1] [0 0 1 1 0 2 0 0 0 1 0 1] [0 0 0 1 1 0 0 0 0 1 1 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 94 sigma_94 = (0,18,12)(1,19,13)(2,17,14)(3,10,23)(4,7,21)(5,20,15)(6,22,9)(8,11,16) alpha_94 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_94 = (0,18,9,7,1,19,4,11,10,6)(2,17,15,23,8,5)(3,20,16,21,22)(12)(13)(14) Aut(G_94) = 1 edge-face adjacency matrix [1 1 0 0 1 0 2 2 0 1 1 1] [0 0 1 1 0 2 0 0 1 0 0 1] [0 0 0 1 1 0 0 0 1 1 1 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 95 sigma_95 = (0,18,12)(1,6,21)(2,17,14)(3,20,7)(4,10,23)(5,19,15)(8,11,16)(9,22,13) alpha_95 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_95 = (0,18,1,22,4,11,10,9,6)(2,17,15,7,5)(3,19,20,16,23,8)(12)(13,21)(14) Aut(G_95) = 1 edge-face adjacency matrix [1 1 0 0 1 0 2 0 0 1 2 1] [0 0 1 1 0 2 0 1 0 0 0 0] [0 0 0 1 1 0 0 1 2 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 96 sigma_96 = (0,18,12)(1,21,13)(2,17,14)(3,20,7)(4,10,23)(5,19,15)(6,22,9)(8,11,16) alpha_96 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_96 = (0,18,9,1,21,22,4,11,10,6)(2,17,15,7,5)(3,19,20,16,23,8)(12)(13)(14) Aut(G_96) = 1 edge-face adjacency matrix [1 1 0 0 1 0 2 0 0 2 2 1] [0 0 1 1 0 2 0 1 0 0 0 0] [0 0 0 1 1 0 0 1 2 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 97 sigma_97 = (0,18,12)(1,21,13)(2,17,14)(3,20,7)(4,9,22)(5,19,15)(6,23,10)(8,11,16) alpha_97 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_97 = (0,18,10,9,1,21,4,11,6)(2,17,15,7,5)(3,19,20,16,22,23,8)(12)(13)(14) Aut(G_97) = 1 edge-face adjacency matrix [1 1 0 0 1 0 2 0 0 2 1 1] [0 0 1 1 0 2 0 1 0 0 0 0] [0 0 0 1 1 0 0 1 2 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 98 sigma_98 = (0,8,21)(1,18,13)(2,17,14)(3,10,23)(4,6,22)(5,19,15)(7,20,16)(9,11,12) alpha_98 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_98 = (0,11,10,6,1,18,4,20)(2,17,15,23,9,8,7,5)(3,19,16,22)(12,21)(13)(14) Aut(G_98) = C2 edge-face adjacency matrix [1 1 0 0 1 0 2 0 1 0 1 1] [0 0 1 1 0 2 0 1 1 1 0 1] [0 0 0 1 1 0 0 1 0 0 1 0] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 99 sigma_99 = (0,16,21)(1,18,13)(2,17,14)(3,20,7)(4,6,11)(5,19,15)(8,22,9)(10,23,12) alpha_99 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_99 = (0,23,6,1,18,4)(2,17,15,7,5)(3,19,20,9,16,11,10,8)(12,21,22)(13)(14) Aut(G_99) = 1 edge-face adjacency matrix [1 1 0 0 1 0 2 0 0 0 0 1] [0 0 1 1 0 2 0 1 0 0 0 0] [0 0 0 1 1 0 0 1 2 1 1 1] [1 0 0 0 0 0 0 0 0 1 1 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 100 sigma_100 = (0,16,21)(1,18,13)(2,17,14)(3,20,7)(4,6,11)(5,19,15)(8,23,10)(9,22,12) alpha_100 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_100 = (0,22,23,6,1,18,4)(2,17,15,7,5)(3,19,20,10,9,16,11,8)(12,21)(13)(14) Aut(G_100) = 1 edge-face adjacency matrix [1 1 0 0 1 0 2 0 0 0 1 1] [0 0 1 1 0 2 0 1 0 0 0 0] [0 0 0 1 1 0 0 1 2 1 1 1] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 101 sigma_101 = (0,16,21)(1,17,13)(2,3,18)(4,5,11)(6,19,14)(7,20,15)(8,22,9)(10,23,12) alpha_101 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_101 = (0,23,5,1,17,4)(2,19,15)(3,20,9,16,11,10,8,7,6)(12,21,22)(13)(14,18) Aut(G_101) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 0 0 0 0 1] [0 0 1 1 0 0 0 1 0 0 0 0] [0 0 0 1 1 0 1 1 2 1 1 1] [1 0 0 0 0 0 0 0 0 1 1 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 102 sigma_102 = (0,16,21)(1,17,13)(2,3,18)(4,5,11)(6,19,14)(7,20,15)(8,23,10)(9,22,12) alpha_102 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_102 = (0,22,23,5,1,17,4)(2,19,15)(3,20,10,9,16,11,8,7,6)(12,21)(13)(14,18) Aut(G_102) = 1 edge-face adjacency matrix [1 1 0 0 1 2 0 0 0 0 1 1] [0 0 1 1 0 0 0 1 0 0 0 0] [0 0 0 1 1 0 1 1 2 1 1 1] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 103 sigma_103 = (0,15,18)(1,4,20)(2,5,19)(3,16,17)(6,22,12)(7,21,14)(8,11,13)(9,23,10) alpha_103 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_103 = (0,22,23,8,4,3)(1,11,9,7,5,16)(2,21,10,6,15,17)(12,18)(13,20)(14,19) Aut(G_103) = S3 edge-face adjacency matrix [1 0 0 1 1 0 0 0 1 0 1 1] [0 1 0 0 1 1 0 1 0 1 0 1] [0 0 1 1 0 1 1 0 0 1 1 0] [1 0 0 0 0 0 1 0 0 0 0 0] [0 1 0 0 0 0 0 0 1 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 104 sigma_104 = (0,7,20)(1,4,22)(2,3,17)(5,18,14)(6,19,15)(8,21,12)(9,23,10)(11,16,13) alpha_104 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_104 = (0,21,10,4,11,9,8,7,6,5,3,19)(1,16)(2,18,15)(12,20)(13,22,23)(14,17) Aut(G_104) = C2 edge-face adjacency matrix [1 0 0 1 1 1 1 2 1 2 1 1] [0 1 0 0 1 0 0 0 0 0 0 0] [0 0 1 1 0 0 1 0 0 0 0 0] [1 0 0 0 0 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 1 1] [0 0 1 0 0 1 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 105 sigma_105 = (0,15,18)(1,8,21)(2,17,14)(3,11,5)(4,7,20)(6,19,12)(9,22,13)(10,23,16) alpha_105 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_105 = (0,19,4,23,3)(1,22,16,20)(2,17,11,10,9,8,7,6,15,5)(12,18)(13,21)(14) Aut(G_105) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 1 0 0 0 1] [0 1 0 0 1 0 0 0 1 0 1 0] [0 0 1 1 0 2 1 1 1 1 1 1] [1 0 0 0 0 0 1 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 106 sigma_106 = (0,15,19)(1,4,18)(2,17,14)(3,11,5)(6,8,21)(7,20,12)(9,22,13)(10,23,16) alpha_106 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_106 = (0,20,6,4,23,3)(1,22,16)(2,17,11,10,9,8,7,15,5)(12,19)(13,18,21)(14) Aut(G_106) = 1 edge-face adjacency matrix [1 0 0 1 1 0 1 0 1 0 0 1] [0 1 0 0 1 0 0 0 0 0 1 0] [0 0 1 1 0 2 0 1 1 1 1 1] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 1 0 0 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 107 sigma_107 = (0,18,12)(1,7,20)(2,17,14)(3,10,23)(4,6,19)(5,11,15)(8,21,13)(9,22,16) alpha_107 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_107 = (0,18,4,22,3,11,10,9,8,7,6)(1,21,16,19)(2,17,15,23,5)(12)(13,20)(14) Aut(G_107) = 1 edge-face adjacency matrix [1 0 0 1 1 0 2 1 1 1 2 1] [0 1 0 0 1 0 0 1 0 1 0 0] [0 0 1 1 0 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 1 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 108 sigma_108 = (0,18,12)(1,4,19)(2,17,14)(3,10,23)(5,11,15)(6,20,7)(8,21,13)(9,22,16) alpha_108 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_108 = (0,18,7,4,22,3,11,10,9,8,6)(1,21,16)(2,17,15,23,5)(12)(13,19,20)(14) Aut(G_108) = 1 edge-face adjacency matrix [1 0 0 1 1 0 2 1 1 1 2 1] [0 1 0 0 1 0 0 0 0 1 0 0] [0 0 1 1 0 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 1 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 109 sigma_109 = (0,18,12)(1,4,19)(2,17,14)(3,10,23)(5,11,15)(6,22,9)(7,20,13)(8,21,16) alpha_109 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_109 = (0,18,9,8,7,4,21,22,3,11,10,6)(1,20,16)(2,17,15,23,5)(12)(13,19)(14) Aut(G_109) = 1 edge-face adjacency matrix [1 0 0 1 1 0 2 1 1 2 2 1] [0 1 0 0 1 0 0 0 1 0 0 0] [0 0 1 1 0 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 110 sigma_110 = (0,18,12)(1,4,19)(2,17,14)(3,22,5)(6,15,11)(7,20,13)(8,21,16)(9,23,10) alpha_110 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_110 = (0,18,11,9,8,7,4,21,10,3,6)(1,20,16)(2,17,22,23,15,5)(12)(13,19)(14) Aut(G_110) = 1 edge-face adjacency matrix [1 0 0 1 1 0 2 1 1 2 1 1] [0 1 0 0 1 0 0 0 1 0 0 0] [0 0 1 1 0 2 0 0 0 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 111 sigma_111 = (0,18,12)(1,4,19)(2,17,14)(3,10,23)(5,11,15)(6,21,8)(7,20,13)(9,22,16) alpha_111 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_111 = (0,18,8,7,4,22,3,11,10,9,6)(1,20,21,16)(2,17,15,23,5)(12)(13,19)(14) Aut(G_111) = 1 edge-face adjacency matrix [1 0 0 1 1 0 2 1 1 1 2 1] [0 1 0 0 1 0 0 0 1 1 0 0] [0 0 1 1 0 2 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 112 sigma_112 = (0,8,21)(1,18,13)(2,17,14)(3,20,7)(4,10,23)(5,19,15)(6,11,16)(9,22,12) alpha_112 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_112 = (0,22,4,11,10,9,8,3,19,20)(1,18,16,23,6)(2,17,15,7,5)(12,21)(13)(14) Aut(G_112) = C2 edge-face adjacency matrix [1 0 0 1 1 0 0 1 2 1 2 1] [0 1 0 0 1 0 2 0 0 0 0 1] [0 0 1 1 0 2 0 1 0 0 0 0] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 113 sigma_113 = (0,7,21)(1,18,13)(2,17,14)(3,16,11)(4,20,6)(5,19,15)(8,10,23)(9,22,12) alpha_113 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_113 = (0,22,8,4,3,19)(1,18,20,23,16,6)(2,17,15,11,10,9,7,5)(12,21)(13)(14) Aut(G_113) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 1 1 0 1 0] [0 1 0 0 1 0 2 0 1 0 0 1] [0 0 1 1 0 2 0 1 0 1 1 1] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 114 sigma_114 = (0,15,19)(1,18,13)(2,17,14)(3,21,8)(4,22,6)(5,20,7)(9,16,23)(10,12,11) alpha_114 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_114 = (0,10,4,9,3)(1,18,22,11,16,6)(2,17,7,15,8,5)(12,19,20,21,23)(13)(14) Aut(G_114) = C2 edge-face adjacency matrix [1 0 0 1 1 0 0 0 0 1 1 0] [0 1 0 0 1 0 2 0 0 0 1 1] [0 0 1 1 0 2 0 1 1 0 0 0] [1 0 0 0 0 0 0 1 1 1 0 1] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 115 sigma_115 = (0,15,19)(1,18,13)(2,17,14)(3,21,8)(4,12,22)(5,20,7)(6,10,23)(9,16,11) alpha_115 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_115 = (0,4,9,3)(1,18,23,16,22,6)(2,17,7,15,8,5)(10,12,19,20,21,11)(13)(14) Aut(G_115) = C2 edge-face adjacency matrix [1 0 0 1 1 0 0 0 0 1 0 0] [0 1 0 0 1 0 2 0 0 0 1 1] [0 0 1 1 0 2 0 1 1 0 0 0] [1 0 0 0 0 0 0 1 1 1 1 1] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 116 sigma_116 = (0,15,19)(1,18,13)(2,17,14)(3,8,11)(4,10,23)(5,21,7)(6,20,16)(9,22,12) alpha_116 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_116 = (0,22,4,20,3)(1,18,16,23,8,6)(2,17,7,15,11,10,9,5)(12,19,21)(13)(14) Aut(G_116) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 0 1 0 1 0] [0 1 0 0 1 0 2 0 1 0 0 1] [0 0 1 1 0 2 0 1 0 1 1 1] [1 0 0 0 0 0 0 1 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 117 sigma_117 = (0,15,19)(1,18,13)(2,17,14)(3,8,11)(4,10,23)(5,22,9)(6,20,16)(7,21,12) alpha_117 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_117 = (0,21,22,4,20,3)(1,18,16,23,8,6)(2,17,9,7,15,11,10,5)(12,19)(13)(14) Aut(G_117) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 0 1 1 1 0] [0 1 0 0 1 0 2 0 1 0 0 1] [0 0 1 1 0 2 0 1 0 1 1 1] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 118 sigma_118 = (0,15,19)(1,18,13)(2,17,14)(3,8,21)(4,10,23)(5,9,11)(6,20,16)(7,22,12) alpha_118 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_118 = (0,22,4,20,3)(1,18,16,23,9,8,6)(2,17,11,10,7,15,21,5)(12,19)(13)(14) Aut(G_118) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 0 1 0 1 0] [0 1 0 0 1 0 2 0 1 1 0 1] [0 0 1 1 0 2 0 1 0 1 1 1] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 119 sigma_119 = (0,19,12)(1,18,13)(2,17,14)(3,20,5)(4,10,23)(6,11,16)(7,9,22)(8,21,15) alpha_119 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_119 = (0,19,22,4,11,10,9,8,3,21,7)(1,18,16,23,6)(2,17,20,15,5)(12)(13)(14) Aut(G_119) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 2 1 2 2 1] [0 1 0 0 1 0 2 0 0 0 0 1] [0 0 1 1 0 2 0 0 1 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 120 sigma_120 = (0,19,12)(1,18,13)(2,17,14)(3,20,5)(4,7,22)(6,11,16)(8,21,15)(9,23,10) alpha_120 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_120 = (0,19,4,11,9,8,3,21,10,7)(1,18,16,22,23,6)(2,17,20,15,5)(12)(13)(14) Aut(G_120) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 2 1 2 1 1] [0 1 0 0 1 0 2 0 0 0 1 1] [0 0 1 1 0 2 0 0 1 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 121 sigma_121 = (0,19,12)(1,18,13)(2,17,14)(3,22,5)(4,20,6)(7,15,11)(8,21,16)(9,23,10) alpha_121 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_121 = (0,19,11,9,8,4,21,10,3,7)(1,18,20,16,6)(2,17,22,23,15,5)(12)(13)(14) Aut(G_121) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 2 1 2 1 1] [0 1 0 0 1 0 2 0 1 0 0 0] [0 0 1 1 0 2 0 0 0 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 122 sigma_122 = (0,19,12)(1,18,13)(2,17,14)(3,16,20)(4,10,23)(5,8,21)(6,11,9)(7,15,22) alpha_122 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_122 = (0,19,22,4,3,7)(1,18,9,8,16,23,6)(2,17,21,11,10,15,20,5)(12)(13)(14) Aut(G_122) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 2 0 0 1 0] [0 1 0 0 1 0 2 0 1 1 0 1] [0 0 1 1 0 2 0 0 1 1 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 123 sigma_123 = (0,19,12)(1,18,13)(2,17,14)(3,16,20)(4,10,23)(5,9,11)(6,21,8)(7,15,22) alpha_123 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_123 = (0,19,22,4,3,7)(1,18,8,16,23,9,6)(2,17,11,10,15,20,21,5)(12)(13)(14) Aut(G_123) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 2 0 0 1 0] [0 1 0 0 1 0 2 0 1 1 0 1] [0 0 1 1 0 2 0 0 1 1 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 124 sigma_124 = (0,19,12)(1,18,13)(2,17,14)(3,16,20)(4,7,11)(5,22,15)(6,21,8)(9,23,10) alpha_124 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_124 = (0,19,4,3,22,23,7)(1,18,8,16,11,9,6)(2,17,15,20,21,10,5)(12)(13)(14) Aut(G_124) = C3 edge-face adjacency matrix [1 0 0 1 1 0 0 2 0 0 1 1] [0 1 0 0 1 0 2 0 1 1 0 1] [0 0 1 1 0 2 0 0 1 1 1 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 125 sigma_125 = (0,8,21)(1,18,13)(2,17,14)(3,16,19)(4,10,23)(5,20,15)(6,11,7)(9,22,12) alpha_125 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_125 = (0,22,4,3,20)(1,18,7,16,23,6)(2,17,15,19,11,10,9,8,5)(12,21)(13)(14) Aut(G_125) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 0 1 0 1 0] [0 1 0 0 1 0 2 1 0 0 0 1] [0 0 1 1 0 2 0 1 1 1 1 1] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 126 sigma_126 = (0,15,20)(1,18,13)(2,17,14)(3,16,19)(4,10,23)(5,21,8)(6,11,7)(9,22,12) alpha_126 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_126 = (0,22,4,3)(1,18,7,16,23,6)(2,17,8,15,19,11,10,9,5)(12,20,21)(13)(14) Aut(G_126) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 0 0 0 1 0] [0 1 0 0 1 0 2 1 0 0 0 1] [0 0 1 1 0 2 0 1 1 1 1 1] [1 0 0 0 0 0 0 0 1 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 127 sigma_127 = (0,15,20)(1,18,13)(2,17,14)(3,16,19)(4,10,23)(5,22,9)(6,11,7)(8,21,12) alpha_127 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_127 = (0,21,22,4,3)(1,18,7,16,23,6)(2,17,9,8,15,19,11,10,5)(12,20)(13)(14) Aut(G_127) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 0 0 1 1 0] [0 1 0 0 1 0 2 1 0 0 0 1] [0 0 1 1 0 2 0 1 1 1 1 1] [1 0 0 0 0 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 128 sigma_128 = (0,15,21)(1,18,13)(2,17,14)(3,16,19)(4,10,23)(5,7,20)(6,11,8)(9,22,12) alpha_128 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_128 = (0,22,4,3)(1,18,8,7,16,23,6)(2,17,20,11,10,9,15,19,5)(12,21)(13)(14) Aut(G_128) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 0 0 0 1 0] [0 1 0 0 1 0 2 1 1 0 0 1] [0 0 1 1 0 2 0 1 1 1 1 1] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 129 sigma_129 = (0,15,21)(1,18,13)(2,17,14)(3,16,19)(4,10,23)(5,8,11)(6,20,7)(9,22,12) alpha_129 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_129 = (0,22,4,3)(1,18,7,16,23,8,6)(2,17,11,10,9,15,19,20,5)(12,21)(13)(14) Aut(G_129) = 1 edge-face adjacency matrix [1 0 0 1 1 0 0 0 0 0 1 0] [0 1 0 0 1 0 2 1 1 0 0 1] [0 0 1 1 0 2 0 1 1 1 1 1] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 130 sigma_130 = (0,17,12)(1,4,18)(2,3,21)(5,15,11)(6,19,13)(7,20,16)(8,22,9)(10,23,14) alpha_130 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_130 = (0,17,11,10,8,7,6,4,20,9,3,5)(1,19,16)(2,23,15)(12)(13,18)(14,21,22) Aut(G_130) = 1 edge-face adjacency matrix [1 0 0 1 1 2 1 1 2 1 1 1] [0 1 0 0 1 0 0 1 0 0 0 0] [0 0 1 1 0 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 1 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 131 sigma_131 = (0,17,12)(1,4,18)(2,3,21)(5,15,11)(6,19,13)(7,20,16)(8,23,10)(9,22,14) alpha_131 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_131 = (0,17,11,8,7,6,4,20,10,9,3,5)(1,19,16)(2,22,23,15)(12)(13,18)(14,21) Aut(G_131) = 1 edge-face adjacency matrix [1 0 0 1 1 2 1 1 2 1 1 1] [0 1 0 0 1 0 0 1 0 0 0 0] [0 0 1 1 0 0 0 0 0 0 1 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 1 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 132 sigma_132 = (0,17,12)(1,4,21)(2,3,18)(5,22,9)(6,19,14)(7,20,15)(8,23,10)(11,16,13) alpha_132 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_132 = (0,17,9,4,11,8,7,6,3,20,10,5)(1,16)(2,19,15)(12)(13,21,22,23)(14,18) Aut(G_132) = 1 edge-face adjacency matrix [1 0 0 1 1 2 1 1 2 1 1 1] [0 1 0 0 1 0 0 0 0 0 0 0] [0 0 1 1 0 0 0 1 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 1 1] [0 0 1 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 133 sigma_133 = (0,17,12)(1,4,22)(2,3,18)(5,8,21)(6,19,14)(7,20,15)(9,23,10)(11,16,13) alpha_133 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_133 = (0,17,21,10,4,11,9,8,7,6,3,20,5)(1,16)(2,19,15)(12)(13,22,23)(14,18) Aut(G_133) = 1 edge-face adjacency matrix [1 0 0 1 1 2 1 1 2 2 1 1] [0 1 0 0 1 0 0 0 0 0 0 0] [0 0 1 1 0 0 0 1 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 1 1] [0 0 1 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 134 sigma_134 = (0,8,21)(1,17,13)(2,3,18)(4,10,23)(5,11,16)(6,19,14)(7,20,15)(9,22,12) alpha_134 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_134 = (0,22,4,11,10,9,8,7,6,3,20)(1,17,16,23,5)(2,19,15)(12,21)(13)(14,18) Aut(G_134) = 1 edge-face adjacency matrix [1 0 0 1 1 0 1 1 2 1 2 1] [0 1 0 0 1 2 0 0 0 0 0 1] [0 0 1 1 0 0 0 1 0 0 0 0] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 135 sigma_135 = (0,18,12)(1,17,13)(2,3,19)(4,10,23)(5,11,16)(6,9,22)(7,20,14)(8,21,15) alpha_135 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_135 = (0,18,22,4,11,10,9,8,7,3,21,6)(1,17,16,23,5)(2,20,15)(12)(13)(14,19) Aut(G_135) = 1 edge-face adjacency matrix [1 0 0 1 1 0 2 1 1 2 2 1] [0 1 0 0 1 2 0 0 0 0 0 1] [0 0 1 1 0 0 0 0 1 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 136 sigma_136 = (0,18,12)(1,17,13)(2,3,19)(4,6,22)(5,11,16)(7,20,14)(8,21,15)(9,23,10) alpha_136 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_136 = (0,18,4,11,9,8,7,3,21,10,6)(1,17,16,22,23,5)(2,20,15)(12)(13)(14,19) Aut(G_136) = 1 edge-face adjacency matrix [1 0 0 1 1 0 2 1 1 2 1 1] [0 1 0 0 1 2 0 0 0 0 1 1] [0 0 1 1 0 0 0 0 1 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 137 sigma_137 = (0,5,19)(1,8,21)(2,16,18)(3,4,17)(6,15,20)(7,14,22)(9,11,13)(10,23,12) alpha_137 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_137 = (0,23,9,8,15,17)(1,11,10,14,18,20)(2,7,5,4)(3,6,16)(12,19,22)(13,21) Aut(G_137) = C2 edge-face adjacency matrix [1 0 0 1 0 1 0 0 1 1 0 1] [0 1 1 0 0 0 1 0 1 0 1 1] [0 0 1 0 1 1 0 1 0 0 0 0] [0 0 0 1 1 0 1 0 0 0 0 0] [1 0 0 0 0 0 0 1 0 0 1 0] [0 1 0 0 0 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 138 sigma_138 = (0,5,19)(1,8,21)(2,16,18)(3,4,17)(6,15,20)(7,11,12)(9,22,13)(10,23,14) alpha_138 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_138 = (0,11,10,9,8,15,17)(1,22,14,18,20)(2,23,7,5,4)(3,6,16)(12,19)(13,21) Aut(G_138) = 1 edge-face adjacency matrix [1 0 0 1 0 1 0 0 1 1 1 1] [0 1 1 0 0 0 1 0 1 0 1 0] [0 0 1 0 1 1 0 1 0 0 0 1] [0 0 0 1 1 0 1 0 0 0 0 0] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 139 sigma_139 = (0,5,19)(1,6,20)(2,16,18)(3,4,17)(7,14,21)(8,15,22)(9,13,23)(10,12,11) alpha_139 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_139 = (0,10,15,17)(1,9,14,18)(2,7,5,4)(3,8,6,16)(11,13,20,22)(12,19,21,23) Aut(G_139) = S4 edge-face adjacency matrix [1 0 0 1 0 1 0 0 0 0 1 0] [0 1 1 0 0 0 1 0 0 1 0 0] [0 0 1 0 1 1 0 1 0 0 0 0] [0 0 0 1 1 0 1 0 1 0 0 0] [0 1 0 0 0 0 0 0 1 0 1 1] [1 0 0 0 0 0 0 1 0 1 0 1] -------------------------------------------------------------------------------- ribbon graph 140 sigma_140 = (0,5,19)(1,6,20)(2,16,18)(3,4,17)(7,14,21)(8,15,22)(9,11,12)(10,23,13) alpha_140 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_140 = (0,11,10,15,17)(1,23,9,14,18)(2,7,5,4)(3,8,6,16)(12,19,21)(13,20,22) Aut(G_140) = C2 edge-face adjacency matrix [1 0 0 1 0 1 0 0 0 0 1 1] [0 1 1 0 0 0 1 0 0 1 0 1] [0 0 1 0 1 1 0 1 0 0 0 0] [0 0 0 1 1 0 1 0 1 0 0 0] [1 0 0 0 0 0 0 1 0 1 0 0] [0 1 0 0 0 0 0 0 1 0 1 0] -------------------------------------------------------------------------------- ribbon graph 141 sigma_141 = (0,5,19)(1,6,20)(2,16,18)(3,4,17)(7,14,21)(8,11,13)(9,22,12)(10,23,15) alpha_141 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_141 = (0,22,15,17)(1,11,10,9,14,18)(2,7,5,4)(3,23,8,6,16)(12,19,21)(13,20) Aut(G_141) = 1 edge-face adjacency matrix [1 0 0 1 0 1 0 0 0 0 1 0] [0 1 1 0 0 0 1 0 0 1 1 1] [0 0 1 0 1 1 0 1 0 0 0 0] [0 0 0 1 1 0 1 0 1 0 0 1] [1 0 0 0 0 0 0 1 0 1 0 0] [0 1 0 0 0 0 0 0 1 0 0 0] -------------------------------------------------------------------------------- ribbon graph 142 sigma_142 = (0,3,17)(1,2,18)(4,19,5)(6,16,20)(7,22,12)(8,21,13)(9,11,14)(10,23,15) alpha_142 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_142 = (0,22,15)(1,21,14)(2,11,10,7,4,6)(3,23,9,8,16,5)(12,17,19)(13,18,20) Aut(G_142) = C2 x C2 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 0 1 0] [0 1 1 0 0 0 0 0 0 1 0 0] [0 0 1 0 1 0 1 1 0 0 1 1] [0 0 0 1 1 1 0 0 1 1 0 1] [1 0 0 0 0 1 0 1 0 0 0 0] [0 1 0 0 0 0 1 0 1 0 0 0] -------------------------------------------------------------------------------- ribbon graph 143 sigma_143 = (0,3,17)(1,2,18)(4,22,8)(5,20,12)(6,19,13)(7,16,21)(9,11,14)(10,23,15) alpha_143 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_143 = (0,20,22,15)(1,19,21,14)(2,11,10,4,7,6)(3,23,9,16,8,5)(12,17)(13,18) Aut(G_143) = C2 edge-face adjacency matrix [1 0 0 1 0 0 0 0 1 0 1 0] [0 1 1 0 0 0 0 1 0 1 0 0] [0 0 1 0 1 0 1 1 0 0 1 1] [0 0 0 1 1 1 0 0 1 1 0 1] [1 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 144 sigma_144 = (0,3,17)(1,2,18)(4,14,20)(5,8,21)(6,19,13)(7,22,9)(10,16,23)(11,15,12) alpha_144 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_144 = (0,15)(1,19,9,8,14)(2,4,10,7,6)(3,11,16,20,5)(12,17,21,22,23)(13,18) Aut(G_144) = C2 x C2 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 0 0 0] [0 1 1 0 0 0 0 1 1 1 0 0] [0 0 1 0 1 0 1 1 0 0 1 0] [0 0 0 1 1 1 0 0 1 0 0 1] [1 0 0 0 0 1 0 0 0 1 1 1] [0 1 0 0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 145 sigma_145 = (0,3,17)(1,8,21)(2,6,20)(4,19,5)(7,11,12)(9,22,13)(10,23,14)(15,18,16) alpha_145 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_145 = (0,11,10,9,8,6,15)(1,22,14,20)(2,23,7,4,18)(3,16,5)(12,17,19)(13,21) Aut(G_145) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 0 1 1 1 1] [0 1 1 0 0 0 0 0 1 0 1 0] [0 0 1 0 1 0 1 1 0 0 0 1] [0 0 0 1 1 1 0 0 0 0 0 0] [1 0 0 0 0 1 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 146 sigma_146 = (0,3,17)(1,7,20)(2,6,19)(4,10,23)(5,11,12)(8,21,13)(9,22,14)(15,18,16) alpha_146 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_146 = (0,11,10,9,8,7,6,15)(1,21,14,19)(2,22,4,18)(3,16,23,5)(12,17)(13,20) Aut(G_146) = C2 edge-face adjacency matrix [1 0 0 1 0 0 1 1 1 1 1 1] [0 1 1 0 0 0 0 1 0 1 0 0] [0 0 1 0 1 0 1 0 0 0 1 0] [0 0 0 1 1 1 0 0 0 0 0 1] [1 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 1 0 0 0] -------------------------------------------------------------------------------- ribbon graph 147 sigma_147 = (0,3,17)(1,8,21)(2,16,20)(4,14,11)(5,18,12)(6,19,15)(7,22,9)(10,23,13) alpha_147 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_147 = (0,18,15)(1,23,14,20)(2,4)(3,19,9,8,16,11,10,7,6,5)(12,17)(13,21,22) Aut(G_147) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 0 0 0 0 0] [0 1 1 0 0 0 0 0 1 0 0 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 1 1 2 1 1 1 1] [1 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 148 sigma_148 = (0,3,17)(1,8,21)(2,16,20)(4,14,11)(5,18,12)(6,19,15)(7,23,10)(9,22,13) alpha_148 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_148 = (0,18,15)(1,22,23,14,20)(2,4)(3,19,10,9,8,16,11,7,6,5)(12,17)(13,21) Aut(G_148) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 0 0 0 0 0] [0 1 1 0 0 0 0 0 1 0 1 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 1 1 2 1 1 1 1] [1 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 149 sigma_149 = (0,3,17)(1,2,20)(4,11,7)(5,18,12)(6,19,15)(8,16,21)(9,22,13)(10,23,14) alpha_149 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_149 = (0,18,15)(1,22,14)(2,23,4,8)(3,19,11,10,9,16,7,6,5)(12,17)(13,20,21) Aut(G_149) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 0 0 0 0 0] [0 1 1 0 0 0 0 0 0 0 1 0] [0 0 1 0 1 0 0 0 1 0 0 1] [0 0 0 1 1 1 1 2 0 1 1 1] [1 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 1 1 0 0] -------------------------------------------------------------------------------- ribbon graph 150 sigma_150 = (0,3,17)(1,2,20)(4,11,7)(5,18,12)(6,19,15)(8,21,13)(9,16,22)(10,23,14) alpha_150 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_150 = (0,18,15)(1,21,22,14)(2,23,4,9,8)(3,19,11,10,16,7,6,5)(12,17)(13,20) Aut(G_150) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 0 0 0 0 0] [0 1 1 0 0 0 0 0 0 1 1 0] [0 0 1 0 1 0 0 0 1 1 0 1] [0 0 0 1 1 1 1 2 0 0 1 1] [1 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 1 0 0 0] -------------------------------------------------------------------------------- ribbon graph 151 sigma_151 = (0,3,17)(1,2,20)(4,10,23)(5,18,12)(6,19,15)(7,11,16)(8,21,13)(9,22,14) alpha_151 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_151 = (0,18,15)(1,21,14)(2,22,4,11,10,9,8)(3,19,16,23,7,6,5)(12,17)(13,20) Aut(G_151) = C2 edge-face adjacency matrix [1 0 0 1 0 0 1 0 0 0 0 0] [0 1 1 0 0 0 0 0 0 1 0 0] [0 0 1 0 1 0 0 0 1 1 2 1] [0 0 0 1 1 1 1 2 0 0 0 1] [1 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 1 0 0 0] -------------------------------------------------------------------------------- ribbon graph 152 sigma_152 = (0,6,19)(1,8,21)(2,5,20)(3,4,18)(7,11,12)(9,22,13)(10,23,14)(15,17,16) alpha_152 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_152 = (0,11,10,9,8,5,15,18)(1,22,14,20)(2,23,7,6,4,17)(3,16)(12,19)(13,21) Aut(G_152) = 1 edge-face adjacency matrix [1 0 0 1 0 1 1 0 1 1 1 1] [0 1 1 0 0 0 0 0 1 0 1 0] [0 0 1 0 1 1 1 1 0 0 0 1] [0 0 0 1 1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 153 sigma_153 = (0,6,19)(1,17,13)(2,11,5)(3,4,18)(7,14,20)(8,21,12)(9,22,15)(10,23,16) alpha_153 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_153 = (0,21,15,18)(1,17,11,10,9,8,14,5)(2,7,6,4,23)(3,22,16)(12,19,20)(13) Aut(G_153) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 0 0 1 0 0] [0 1 1 0 0 2 0 0 1 1 1 1] [0 0 1 0 1 0 1 1 0 0 0 1] [0 0 0 1 1 0 0 0 0 0 1 0] [1 0 0 0 0 0 0 1 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 154 sigma_154 = (0,6,19)(1,17,13)(2,10,23)(3,4,18)(5,11,14)(7,20,12)(8,21,15)(9,22,16) alpha_154 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_154 = (0,20,15,18)(1,17,14,23,5)(2,11,10,9,8,7,6,4,22)(3,21,16)(12,19)(13) Aut(G_154) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 0 1 0 0 0] [0 1 1 0 0 2 0 0 0 0 0 1] [0 0 1 0 1 0 1 1 1 1 2 1] [0 0 0 1 1 0 0 0 0 1 0 0] [1 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 155 sigma_155 = (0,3,18)(1,17,13)(2,11,5)(4,19,6)(7,14,20)(8,21,12)(9,22,15)(10,23,16) alpha_155 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_155 = (0,21,15)(1,17,11,10,9,8,14,5)(2,7,4,23)(3,22,16,6)(12,18,19,20)(13) Aut(G_155) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 1 0 0] [0 1 1 0 0 2 0 0 1 1 1 1] [0 0 1 0 1 0 0 1 0 0 0 1] [0 0 0 1 1 0 1 0 0 0 1 0] [1 0 0 0 0 0 1 1 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 156 sigma_156 = (0,3,18)(1,17,13)(2,11,5)(4,19,6)(7,20,12)(8,14,21)(9,22,15)(10,23,16) alpha_156 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_156 = (0,20,21,15)(1,17,11,10,9,14,5)(2,8,7,4,23)(3,22,16,6)(12,18,19)(13) Aut(G_156) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 1 1 0 0] [0 1 1 0 0 2 0 0 0 1 1 1] [0 0 1 0 1 0 0 1 1 0 0 1] [0 0 0 1 1 0 1 0 0 0 1 0] [1 0 0 0 0 0 1 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 157 sigma_157 = (0,3,18)(1,17,13)(2,10,23)(4,19,6)(5,11,14)(7,20,12)(8,21,15)(9,22,16) alpha_157 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_157 = (0,20,15)(1,17,14,23,5)(2,11,10,9,8,7,4,22)(3,21,16,6)(12,18,19)(13) Aut(G_157) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 1 0 0 0] [0 1 1 0 0 2 0 0 0 0 0 1] [0 0 1 0 1 0 0 1 1 1 2 1] [0 0 0 1 1 0 1 0 0 1 0 0] [1 0 0 0 0 0 1 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 158 sigma_158 = (0,3,18)(1,17,13)(2,16,22)(4,19,6)(5,10,23)(7,20,12)(8,21,15)(9,14,11) alpha_158 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_158 = (0,20,15)(1,17,23,14,22,5)(2,9,8,7,4)(3,21,11,10,16,6)(12,18,19)(13) Aut(G_158) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 1 0 0 0] [0 1 1 0 0 2 0 0 0 0 1 1] [0 0 1 0 1 0 0 1 1 1 0 0] [0 0 0 1 1 0 1 0 0 1 1 1] [1 0 0 0 0 0 1 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 159 sigma_159 = (0,3,18)(1,17,13)(2,22,5)(4,19,6)(7,14,11)(8,21,16)(9,23,10)(12,20,15) alpha_159 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_159 = (0,15)(1,17,22,23,14,5)(2,7,4,21,10)(3,20,16,6)(8,12,18,19,11,9)(13) Aut(G_159) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 0 0 0] [0 1 1 0 0 2 0 0 0 0 1 1] [0 0 1 0 1 0 0 1 0 1 1 0] [0 0 0 1 1 0 1 0 1 0 0 0] [1 0 0 0 0 0 1 1 1 1 0 1] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 160 sigma_160 = (0,3,18)(1,17,13)(2,9,22)(4,19,6)(5,10,23)(7,14,11)(8,21,16)(12,20,15) alpha_160 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_160 = (0,15)(1,17,23,14,22,5)(2,7,4,21)(3,20,16,6)(8,12,18,19,11,10,9)(13) Aut(G_160) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 0 0 0] [0 1 1 0 0 2 0 0 0 0 1 1] [0 0 1 0 1 0 0 1 0 1 0 0] [0 0 0 1 1 0 1 0 1 0 0 0] [1 0 0 0 0 0 1 1 1 1 1 1] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 161 sigma_161 = (0,3,18)(1,17,13)(2,16,21)(4,19,6)(5,9,11)(7,14,22)(8,10,23)(12,20,15) alpha_161 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_161 = (0,15)(1,17,11,10,14,21,5)(2,7,4)(3,20,23,9,16,6)(8,12,18,19,22)(13) Aut(G_161) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 0 0 0] [0 1 1 0 0 2 0 0 0 1 1 1] [0 0 1 0 1 0 0 1 0 0 0 0] [0 0 0 1 1 0 1 0 1 1 0 1] [1 0 0 0 0 0 1 1 1 0 1 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 162 sigma_162 = (0,3,18)(1,17,13)(2,16,11)(4,19,6)(5,21,14)(7,9,22)(8,10,23)(12,20,15) alpha_162 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_162 = (0,15)(1,17,14,11,10,9,5)(2,21,7,4)(3,20,23,16,6)(8,12,18,19,22)(13) Aut(G_162) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 0 0 0] [0 1 1 0 0 2 0 0 0 1 1 1] [0 0 1 0 1 0 0 1 0 1 0 0] [0 0 0 1 1 0 1 0 1 0 0 1] [1 0 0 0 0 0 1 1 1 0 1 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 163 sigma_163 = (0,3,18)(1,17,13)(2,16,11)(4,8,21)(5,20,14)(6,19,12)(7,9,22)(10,23,15) alpha_163 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_163 = (0,19,22,15)(1,17,14,11,10,9,8,5)(2,20,4)(3,23,16,21,7,6)(12,18)(13) Aut(G_163) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 1 0 0 1 0] [0 1 1 0 0 2 0 0 1 1 1 1] [0 0 1 0 1 0 0 0 1 0 0 0] [0 0 0 1 1 0 1 1 0 1 0 1] [1 0 0 0 0 0 1 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 164 sigma_164 = (0,3,18)(1,17,13)(2,10,23)(4,9,11)(5,21,14)(6,19,12)(7,20,15)(8,22,16) alpha_164 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_164 = (0,19,15)(1,17,14,23,9,5)(2,21,4,22)(3,20,16,11,10,8,7,6)(12,18)(13) Aut(G_164) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 1 0 0 0 0] [0 1 1 0 0 2 0 0 0 1 0 1] [0 0 1 0 1 0 0 0 0 1 1 0] [0 0 0 1 1 0 1 1 2 0 1 1] [1 0 0 0 0 0 1 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 165 sigma_165 = (0,3,18)(1,17,13)(2,16,21)(4,14,11)(5,9,22)(6,19,12)(7,20,15)(8,23,10) alpha_165 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_165 = (0,19,15)(1,17,22,23,14,21,5)(2,4)(3,20,10,9,16,11,8,7,6)(12,18)(13) Aut(G_165) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 1 0 0 0 0] [0 1 1 0 0 2 0 0 0 1 1 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 0 1 1 2 1 1 1] [1 0 0 0 0 0 1 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 166 sigma_166 = (0,3,18)(1,17,13)(2,16,11)(4,14,20)(5,22,9)(6,19,12)(7,8,21)(10,23,15) alpha_166 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_166 = (0,19,21,22,15)(1,17,9,8,14,11,10,5)(2,4)(3,23,16,20,7,6)(12,18)(13) Aut(G_166) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 1 0 1 1 0] [0 1 1 0 0 2 0 0 1 1 1 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 0 1 1 1 0 0 1] [1 0 0 0 0 0 1 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 167 sigma_167 = (0,3,18)(1,17,13)(2,16,21)(4,14,20)(5,9,11)(6,19,12)(7,8,22)(10,23,15) alpha_167 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_167 = (0,19,22,15)(1,17,11,10,8,14,21,5)(2,4)(3,23,9,16,20,7,6)(12,18)(13) Aut(G_167) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 1 0 0 1 0] [0 1 1 0 0 2 0 0 1 1 1 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 0 1 1 1 1 0 1] [1 0 0 0 0 0 1 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 168 sigma_168 = (0,3,18)(1,17,13)(2,16,11)(4,14,20)(5,21,8)(6,19,12)(7,9,22)(10,23,15) alpha_168 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_168 = (0,19,22,15)(1,17,8,14,11,10,9,5)(2,4)(3,23,16,20,21,7,6)(12,18)(13) Aut(G_168) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 1 0 0 1 0] [0 1 1 0 0 2 0 0 1 1 1 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 0 1 1 1 1 0 1] [1 0 0 0 0 0 1 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 169 sigma_169 = (0,3,18)(1,17,13)(2,16,11)(4,7,20)(5,19,14)(6,8,21)(9,22,12)(10,23,15) alpha_169 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_169 = (0,22,15)(1,17,14,11,10,9,8,7,5)(2,19,4)(3,23,16,20,6)(12,18,21)(13) Aut(G_169) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 0 1 0] [0 1 1 0 0 2 0 1 1 1 1 1] [0 0 1 0 1 0 0 1 0 0 0 0] [0 0 0 1 1 0 1 0 1 0 0 1] [1 0 0 0 0 0 1 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 170 sigma_170 = (0,3,18)(1,17,13)(2,16,11)(4,14,19)(5,21,8)(6,7,20)(9,22,12)(10,23,15) alpha_170 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_170 = (0,22,15)(1,17,8,7,14,11,10,9,5)(2,4)(3,23,16,19,6)(12,18,20,21)(13) Aut(G_170) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 0 1 0] [0 1 1 0 0 2 0 1 1 1 1 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 0 1 1 0 0 0 1] [1 0 0 0 0 0 1 0 1 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 171 sigma_171 = (0,3,18)(1,17,13)(2,16,11)(4,14,19)(5,22,9)(6,7,20)(8,21,12)(10,23,15) alpha_171 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_171 = (0,21,22,15)(1,17,9,8,7,14,11,10,5)(2,4)(3,23,16,19,6)(12,18,20)(13) Aut(G_171) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 1 1 0] [0 1 1 0 0 2 0 1 1 1 1 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 0 1 1 0 0 0 1] [1 0 0 0 0 0 1 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 172 sigma_172 = (0,3,18)(1,17,13)(2,16,11)(4,14,19)(5,20,7)(6,8,21)(9,22,12)(10,23,15) alpha_172 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_172 = (0,22,15)(1,17,7,14,11,10,9,8,5)(2,4)(3,23,16,19,20,6)(12,18,21)(13) Aut(G_172) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 0 1 0] [0 1 1 0 0 2 0 1 1 1 1 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 0 1 1 1 0 0 1] [1 0 0 0 0 0 1 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 173 sigma_173 = (0,7,20)(1,17,13)(2,6,21)(3,4,19)(5,9,11)(8,14,22)(10,23,12)(15,18,16) alpha_173 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_173 = (0,23,9,6,15,19)(1,17,11,10,14,21,5)(2,8,7,4,18)(3,16)(12,20,22)(13) Aut(G_173) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 1 0 1 0 1] [0 1 1 0 0 2 0 0 0 1 1 1] [0 0 1 0 1 0 1 1 1 0 0 0] [0 0 0 1 1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 1 0 1 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 174 sigma_174 = (0,7,20)(1,17,13)(2,6,21)(3,4,19)(5,9,23)(8,22,12)(10,14,11)(15,18,16) alpha_174 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_174 = (0,22,11,9,6,15,19)(1,17,23,14,21,5)(2,10,8,7,4,18)(3,16)(12,20)(13) Aut(G_174) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 1 0 1 1 1] [0 1 1 0 0 2 0 0 0 1 0 1] [0 0 1 0 1 0 1 1 1 0 1 0] [0 0 0 1 1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 175 sigma_175 = (0,7,20)(1,17,13)(2,16,11)(3,6,19)(4,14,18)(5,21,8)(9,22,12)(10,23,15) alpha_175 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_175 = (0,22,15,19)(1,17,8,7,6,14,11,10,9,5)(2,4)(3,23,16,18)(12,20,21)(13) Aut(G_175) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 1 0 0 1 0] [0 1 1 0 0 2 1 1 1 1 1 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 0 1 0 0 0 0 1] [1 0 0 0 0 0 0 0 1 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 176 sigma_176 = (0,8,21)(1,17,13)(2,16,11)(3,7,20)(4,14,18)(5,19,6)(9,22,12)(10,23,15) alpha_176 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_176 = (0,22,15,20)(1,17,6,14,11,10,9,8,7,5)(2,4)(3,23,16,18,19)(12,21)(13) Aut(G_176) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 1 0 1 0] [0 1 1 0 0 2 1 1 1 1 1 1] [0 0 1 0 1 0 0 0 0 0 0 0] [0 0 0 1 1 0 1 1 0 0 0 1] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 177 sigma_177 = (0,18,12)(1,17,13)(2,9,11)(3,10,23)(4,14,20)(5,22,8)(6,21,7)(15,19,16) alpha_177 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_177 = (0,18,7,15,23,9,6)(1,17,8,14,11,10,5)(2,4,19,21)(3,16,20,22)(12)(13) Aut(G_177) = C2 edge-face adjacency matrix [1 0 0 1 0 0 2 1 0 1 0 1] [0 1 1 0 0 2 0 0 1 0 1 1] [0 0 1 0 1 0 0 1 0 1 0 0] [0 0 0 1 1 0 0 0 1 0 1 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 178 sigma_178 = (0,18,12)(1,17,13)(2,7,21)(3,10,23)(4,14,20)(5,22,8)(6,11,9)(15,19,16) alpha_178 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_178 = (0,18,9,7,15,23,6)(1,17,8,14,21,11,10,5)(2,4,19)(3,16,20,22)(12)(13) Aut(G_178) = 1 edge-face adjacency matrix [1 0 0 1 0 0 2 1 0 1 0 1] [0 1 1 0 0 2 0 0 1 1 1 1] [0 0 1 0 1 0 0 1 0 0 0 0] [0 0 0 1 1 0 0 0 1 0 1 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 179 sigma_179 = (0,18,12)(1,17,13)(2,7,21)(3,8,23)(4,14,20)(5,10,11)(6,22,9)(15,19,16) alpha_179 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_179 = (0,18,9,7,15,23,10,6)(1,17,11,8,14,21,22,5)(2,4,19)(3,16,20)(12)(13) Aut(G_179) = C2 edge-face adjacency matrix [1 0 0 1 0 0 2 1 0 1 1 1] [0 1 1 0 0 2 0 0 1 1 1 1] [0 0 1 0 1 0 0 1 0 0 0 0] [0 0 0 1 1 0 0 0 1 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 180 sigma_180 = (0,18,12)(1,17,13)(2,7,21)(3,8,23)(4,14,20)(5,9,22)(6,11,10)(15,19,16) alpha_180 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_180 = (0,18,10,9,7,15,23,6)(1,17,22,11,8,14,21,5)(2,4,19)(3,16,20)(12)(13) Aut(G_180) = C2 edge-face adjacency matrix [1 0 0 1 0 0 2 1 0 1 1 1] [0 1 1 0 0 2 0 0 1 1 1 1] [0 0 1 0 1 0 0 1 0 0 0 0] [0 0 0 1 1 0 0 0 1 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 181 sigma_181 = (0,18,12)(1,17,13)(2,10,23)(3,9,11)(4,7,21)(5,19,14)(6,22,8)(15,20,16) alpha_181 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_181 = (0,18,8,15,11,10,6)(1,17,14,23,9,7,5)(2,19,4,20,22)(3,16,21)(12)(13) Aut(G_181) = 1 edge-face adjacency matrix [1 0 0 1 0 0 2 0 1 0 1 1] [0 1 1 0 0 2 0 1 0 1 0 1] [0 0 1 0 1 0 0 1 1 0 1 0] [0 0 0 1 1 0 0 0 0 1 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 182 sigma_182 = (0,18,12)(1,17,13)(2,8,21)(3,10,23)(4,7,22)(5,19,14)(6,11,9)(15,20,16) alpha_182 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_182 = (0,18,9,8,15,23,6)(1,17,14,21,11,10,7,5)(2,19,4,20)(3,16,22)(12)(13) Aut(G_182) = 1 edge-face adjacency matrix [1 0 0 1 0 0 2 0 1 1 0 1] [0 1 1 0 0 2 0 1 0 1 1 1] [0 0 1 0 1 0 0 1 1 0 0 0] [0 0 0 1 1 0 0 0 0 0 1 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 183 sigma_183 = (0,18,12)(1,17,13)(2,20,7)(3,10,23)(4,8,22)(5,19,14)(6,21,15)(9,11,16) alpha_183 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_183 = (0,18,15,23,9,6)(1,17,14,7,5)(2,19,20,4,11,10,8)(3,21,16,22)(12)(13) Aut(G_183) = 1 edge-face adjacency matrix [1 0 0 1 0 0 2 0 0 1 0 1] [0 1 1 0 0 2 0 1 0 0 0 0] [0 0 1 0 1 0 0 1 2 0 1 1] [0 0 0 1 1 0 0 0 0 1 1 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 184 sigma_184 = (0,18,12)(1,17,13)(2,20,7)(3,22,9)(4,8,11)(5,19,14)(6,21,15)(10,23,16) alpha_184 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_184 = (0,18,15,9,6)(1,17,14,7,5)(2,19,20,4,23,8)(3,21,22,16,11,10)(12)(13) Aut(G_184) = C2 edge-face adjacency matrix [1 0 0 1 0 0 2 0 0 1 0 0] [0 1 1 0 0 2 0 1 0 0 0 0] [0 0 1 0 1 0 0 1 2 0 0 1] [0 0 0 1 1 0 0 0 0 1 2 1] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 185 sigma_185 = (0,18,12)(1,17,13)(2,20,7)(3,4,22)(5,19,14)(6,21,15)(8,23,10)(9,11,16) alpha_185 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_185 = (0,18,15,22,23,9,6)(1,17,14,7,5)(2,19,20,10,4,11,8)(3,21,16)(12)(13) Aut(G_185) = 1 edge-face adjacency matrix [1 0 0 1 0 0 2 0 0 1 1 1] [0 1 1 0 0 2 0 1 0 0 0 0] [0 0 1 0 1 0 0 1 2 0 1 1] [0 0 0 1 1 0 0 0 0 1 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 186 sigma_186 = (0,18,12)(1,17,13)(2,20,7)(3,4,21)(5,19,14)(6,9,22)(8,23,10)(11,16,15) alpha_186 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_186 = (0,18,22,23,15,21,6)(1,17,14,7,5)(2,19,20,10,9,4,11,8)(3,16)(12)(13) Aut(G_186) = 1 edge-face adjacency matrix [1 0 0 1 0 0 2 0 0 1 1 1] [0 1 1 0 0 2 0 1 0 0 0 0] [0 0 1 0 1 0 0 1 2 1 1 1] [0 0 0 1 1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 187 sigma_187 = (0,18,12)(1,17,13)(2,9,11)(3,10,23)(4,7,22)(5,19,14)(6,20,15)(8,21,16) alpha_187 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_187 = (0,18,15,23,9,8,6)(1,17,14,11,10,7,5)(2,19,4,21)(3,20,16,22)(12)(13) Aut(G_187) = C2 edge-face adjacency matrix [1 0 0 1 0 0 2 0 1 1 0 1] [0 1 1 0 0 2 0 1 0 0 1 1] [0 0 1 0 1 0 0 1 0 1 0 0] [0 0 0 1 1 0 0 0 1 0 1 0] [1 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 188 sigma_188 = (0,8,21)(1,17,13)(2,19,6)(3,4,20)(5,18,14)(7,23,10)(9,22,12)(11,16,15) alpha_188 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_188 = (0,22,23,15,20)(1,17,14,6,5)(2,18,19,10,9,8,4,11,7)(3,16)(12,21)(13) Aut(G_188) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 1 0 1 1] [0 1 1 0 0 2 1 0 0 0 0 0] [0 0 1 0 1 0 1 2 1 1 1 1] [0 0 0 1 1 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 189 sigma_189 = (0,3,20)(1,17,13)(2,19,6)(4,22,9)(5,18,14)(7,23,10)(8,21,12)(11,16,15) alpha_189 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_189 = (0,21,22,23,15)(1,17,14,6,5)(2,18,19,10,4,11,7)(3,16,9,8)(12,20)(13) Aut(G_189) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 1 1 1] [0 1 1 0 0 2 1 0 0 0 0 0] [0 0 1 0 1 0 1 2 0 0 1 1] [0 0 0 1 1 0 0 0 1 1 0 0] [1 0 0 0 0 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 190 sigma_190 = (0,3,20)(1,17,13)(2,19,6)(4,7,11)(5,18,14)(8,21,12)(9,22,15)(10,23,16) alpha_190 = (0,12)(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23) phi_190 = (0,21,15)(1,17,14,6,5)(2,18,19,4,23,7)(3,22,16,11,10,9,8)(12,20)(13) Aut(G_190) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 0 0 1 0 0] [0 1 1 0 0 2 1 0 0 0 0 0] [0 0 1 0 1 0 1 2 0 0 0 1] [0 0 0 1 1 0 0 0 1 1 2 1] [1 0 0 0 0 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] 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