ribbon graph 0 sigma_0 = (0,16,9)(1,7,17)(2,14,11)(3,13,12)(4,5,15)(6,10,8) alpha_0 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_0 = (0,16,1,6,5,2,14,4,3,13,15,8,7)(9)(10,17)(11)(12) Aut(G_0) = 1 edge-face adjacency matrix [1 1 1 1 2 2 2 2 1] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 1] [0 0 1 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 1 sigma_1 = (0,17,9)(1,16,10)(2,14,11)(3,13,12)(4,5,15)(6,7,8) alpha_1 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_1 = (0,17,7,1,16,6,5,2,14,4,3,13,15,8)(9)(10)(11)(12) Aut(G_1) = C2 edge-face adjacency matrix [1 1 1 1 2 2 2 2 2] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 2 sigma_2 = (0,4,15)(1,7,17)(2,14,11)(3,13,12)(5,10,8)(6,16,9) alpha_2 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_2 = (0,16,1,5,2,14,8,7,6,4,3,13)(9,15)(10,17)(11)(12) Aut(G_2) = C2 edge-face adjacency matrix [1 1 1 1 2 2 1 2 1] [1 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 1] [0 0 1 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 3 sigma_3 = (0,4,16)(1,15,10)(2,14,11)(3,13,12)(5,17,7)(6,9,8) alpha_3 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_3 = (0,6,1,15,8,5,2,14,7,4,3,13)(9,16,17)(10)(11)(12) Aut(G_3) = C3 edge-face adjacency matrix [1 1 1 1 2 2 2 1 1] [1 0 0 0 0 0 0 1 1] [0 1 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 4 sigma_4 = (0,13,9)(1,4,14)(2,3,16)(5,15,10)(6,12,8)(7,17,11) alpha_4 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_4 = (0,13,1,15,8,7,3,6,5,4)(2,17,12)(9)(10,14)(11,16) Aut(G_4) = 1 edge-face adjacency matrix [1 1 0 1 2 1 2 1 1] [0 0 1 1 0 0 0 0 1] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 1 0 0 0] [0 0 1 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 5 sigma_5 = (0,13,9)(1,14,10)(2,6,16)(3,5,15)(4,12,8)(7,17,11) alpha_5 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_5 = (0,13,8,7,6,5,1,14,3,4)(2,17,12,15)(9)(10)(11,16) Aut(G_5) = 1 edge-face adjacency matrix [1 1 0 1 2 2 1 1 1] [0 0 1 1 0 0 1 0 1] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 6 sigma_6 = (0,13,9)(1,14,10)(2,3,15)(4,12,8)(5,16,6)(7,17,11) alpha_6 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_6 = (0,13,8,7,5,1,14,6,3,4)(2,17,12)(9)(10)(11,15,16) Aut(G_6) = C2 edge-face adjacency matrix [1 1 0 1 2 2 1 1 1] [0 0 1 1 0 0 0 0 1] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] [0 0 1 0 0 0 1 1 0] -------------------------------------------------------------------------------- ribbon graph 7 sigma_7 = (0,13,9)(1,14,10)(2,3,16)(4,15,5)(6,12,8)(7,17,11) alpha_7 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_7 = (0,13,5,1,14,15,8,7,3,6,4)(2,17,12)(9)(10)(11,16) Aut(G_7) = 1 edge-face adjacency matrix [1 1 0 1 2 2 2 1 1] [0 0 1 1 0 0 0 0 1] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 8 sigma_8 = (0,12,14)(1,6,16)(2,13,11)(3,8,4)(5,15,9)(7,17,10) alpha_8 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_8 = (0,15,1,17,3)(2,13,8,7,6,5,12,4)(9,14)(10,16)(11) Aut(G_8) = 1 edge-face adjacency matrix [1 1 0 1 0 0 1 0 1] [0 0 1 1 2 1 1 1 1] [1 0 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 1 0] [0 0 1 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 9 sigma_9 = (0,14,9)(1,5,15)(2,13,11)(3,7,17)(4,8,12)(6,16,10) alpha_9 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_9 = (0,14,1,16,3,8,7,6,5)(2,13,12,17,4)(9)(10,15)(11) Aut(G_9) = 1 edge-face adjacency matrix [1 1 0 1 0 2 1 2 1] [0 0 1 1 2 0 0 0 1] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 1 0 0] [0 0 1 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 10 sigma_10 = (0,14,9)(1,15,10)(2,13,11)(3,7,17)(4,8,12)(5,16,6) alpha_10 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_10 = (0,14,6,1,15,16,3,8,7,5)(2,13,12,17,4)(9)(10)(11) Aut(G_10) = 1 edge-face adjacency matrix [1 1 0 1 0 2 2 2 1] [0 0 1 1 2 0 0 0 1] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 11 sigma_11 = (0,14,9)(1,15,10)(2,13,11)(3,6,16)(4,8,12)(5,17,7) alpha_11 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_11 = (0,14,7,6,1,15,3,8,5)(2,13,12,16,17,4)(9)(10)(11) Aut(G_11) = 1 edge-face adjacency matrix [1 1 0 1 0 2 2 1 1] [0 0 1 1 2 0 0 1 1] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 12 sigma_12 = (0,4,15)(1,5,16)(2,12,14)(3,11,13)(6,8,9)(7,17,10) alpha_12 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_12 = (0,8,7,5,12,13)(1,17,6,4,11,14)(2,3)(9,15)(10,16) Aut(G_12) = S3 edge-face adjacency matrix [1 0 0 1 1 1 0 1 1] [0 1 1 0 1 1 1 0 1] [0 0 1 1 0 0 0 0 0] [1 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 1 0] -------------------------------------------------------------------------------- ribbon graph 13 sigma_13 = (0,3,13)(1,5,15)(2,12,14)(4,11,16)(6,8,10)(7,17,9) alpha_13 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_13 = (0,17,6,5,12)(1,8,7,11,14)(2,4,3)(9,13,16)(10,15) Aut(G_13) = C2 edge-face adjacency matrix [1 0 0 1 0 1 1 0 1] [0 1 1 0 0 1 0 1 1] [0 0 1 1 1 0 0 0 0] [1 0 0 0 1 0 0 1 0] [0 1 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 14 sigma_14 = (0,3,13)(1,5,15)(2,12,14)(4,17,7)(6,9,16)(8,11,10) alpha_14 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_14 = (0,6,5,12)(1,11,14)(2,8,4,3)(7,9,13)(10,15,16,17) Aut(G_14) = S3 edge-face adjacency matrix [1 0 0 1 0 1 1 0 0] [0 1 1 0 0 1 0 0 0] [0 0 1 1 1 0 0 0 1] [1 0 0 0 1 0 0 1 0] [0 1 0 0 0 0 1 1 1] -------------------------------------------------------------------------------- ribbon graph 15 sigma_15 = (0,3,13)(1,5,15)(2,12,14)(4,8,9)(6,16,10)(7,17,11) alpha_15 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_15 = (0,8,7,6,5,12)(1,16,11,14)(2,17,4,3)(9,13)(10,15) Aut(G_15) = C2 edge-face adjacency matrix [1 0 0 1 0 1 1 1 1] [0 1 1 0 0 1 0 1 0] [0 0 1 1 1 0 0 0 1] [1 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 1 0 0] -------------------------------------------------------------------------------- ribbon graph 16 sigma_16 = (0,3,13)(1,2,16)(4,14,9)(5,15,12)(6,17,7)(8,11,10) alpha_16 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_16 = (0,14,12)(1,11)(2,8,6,5,4,3,15,7)(9,13)(10,16,17) Aut(G_16) = C2 edge-face adjacency matrix [1 0 0 1 0 1 0 0 0] [0 1 1 0 0 0 0 0 0] [0 0 1 1 1 1 2 1 1] [1 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 1 1] -------------------------------------------------------------------------------- ribbon graph 17 sigma_17 = (0,5,15)(1,13,10)(2,12,8)(3,11,14)(4,16,6)(7,17,9) alpha_17 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_17 = (0,17,12,14)(1,13,6,5,11,8,7,4)(2,3)(9,15,16)(10) Aut(G_17) = 1 edge-face adjacency matrix [1 0 0 1 0 1 0 0 1] [0 1 1 0 2 1 1 1 1] [0 0 1 1 0 0 0 0 0] [1 0 0 0 0 0 1 1 0] [0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 18 sigma_18 = (0,3,14)(1,13,10)(2,8,4)(5,11,15)(6,16,9)(7,17,12) alpha_18 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_18 = (0,16,12)(1,13,8,7,6,11,4)(2,5,3,17)(9,14,15)(10) Aut(G_18) = 1 edge-face adjacency matrix [1 0 0 1 0 0 0 1 0] [0 1 1 0 2 0 1 1 1] [0 0 1 1 0 1 0 0 1] [1 0 0 0 0 1 1 0 0] [0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 19 sigma_19 = (0,3,14)(1,13,10)(2,7,17)(4,8,11)(5,15,9)(6,16,12) alpha_19 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_19 = (0,15,12)(1,13,11,17,4)(2,8,7,6,5,3,16)(9,14)(10) Aut(G_19) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 0 0] [0 1 1 0 2 0 0 0 1] [0 0 1 1 0 1 1 2 1] [1 0 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 20 sigma_20 = (0,3,14)(1,13,10)(2,8,4)(5,15,9)(6,11,16)(7,17,12) alpha_20 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_20 = (0,15,16,12)(1,13,8,7,11,4)(2,6,5,3,17)(9,14)(10) Aut(G_20) = 1 edge-face adjacency matrix [1 0 0 1 0 0 1 1 0] [0 1 1 0 2 0 0 1 1] [0 0 1 1 0 1 1 0 1] [1 0 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 21 sigma_21 = (0,14,9)(1,13,10)(2,7,17)(3,16,6)(4,8,11)(5,15,12) alpha_21 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_21 = (0,14,12,6,5)(1,13,11,17,4)(2,8,7,3,15,16)(9)(10) Aut(G_21) = C2 edge-face adjacency matrix [1 0 0 1 0 2 1 0 0] [0 1 1 0 2 0 0 0 1] [0 0 1 1 0 0 1 2 1] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 22 sigma_22 = (0,14,9)(1,13,10)(2,6,8)(3,7,17)(4,16,11)(5,15,12) alpha_22 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_22 = (0,14,12,17,6,5)(1,13,11,8,7,4)(2,16,3,15)(9)(10) Aut(G_22) = C2 edge-face adjacency matrix [1 0 0 1 0 2 1 0 1] [0 1 1 0 2 0 0 1 1] [0 0 1 1 0 0 1 1 0] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 23 sigma_23 = (0,14,9)(1,13,10)(2,12,15)(3,11,17)(4,6,16)(5,8,7) alpha_23 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_23 = (0,14,7,6,12,17,5)(1,13,16,8,11,15,4)(2,3)(9)(10) Aut(G_23) = C2 edge-face adjacency matrix [1 0 0 1 0 2 1 1 1] [0 1 1 0 2 0 1 1 1] [0 0 1 1 0 0 0 0 0] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 24 sigma_24 = (0,14,9)(1,13,10)(2,12,15)(3,7,17)(4,16,11)(5,8,6) alpha_24 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_24 = (0,14,6,12,17,5)(1,13,11,15,8,7,4)(2,16,3)(9)(10) Aut(G_24) = 1 edge-face adjacency matrix [1 0 0 1 0 2 1 0 1] [0 1 1 0 2 0 1 1 1] [0 0 1 1 0 0 0 1 0] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] -------------------------------------------------------------------------------- ribbon graph 25 sigma_25 = (0,14,9)(1,13,10)(2,12,15)(3,11,17)(4,7,8)(5,16,6) alpha_25 = (0,9)(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17) phi_25 = (0,14,6,12,17,7,5)(1,13,8,11,15,16,4)(2,3)(9)(10) Aut(G_25) = C2 edge-face adjacency matrix [1 0 0 1 0 2 1 1 1] [0 1 1 0 2 0 1 1 1] [0 0 1 1 0 0 0 0 0] [1 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] --------------------------------------------------------------------------------