/* * This file contains the list of all prime knots * with up to 11 crossings in PARI/GP format suitable for feeding into KhoHo, * a program by A. Shumakovitch for computing and studying Khovanov homology. * To read from within gp execute `read(KTable_11)' * * This list was converted by A. Shumakovitch from the one supplied * by D. Bar-Natan with his program Categorification.m * According to Bar-Natan, this data was in turn ``provided to [him] by * A. Stoimenow who himself borrowed it from J. Hoste and M. Thistlethwaite, * and was translated to [their] format by a program written by D. Thurston''. * The list is thus not guaranteed to be absolutely complete and/or correct. * * For further info see: * KhoHo: http://www.geometrie.ch/KhoHo * Categorification.m: * http://www.math.toronto.edu/~drorbn/papers/Categorification * Knotscape: http://www.math.utk.edu/~morwen/knotscape.html */ { print1("Loading the table of knots with up to 11 crossings ... "); NumberOfKnots3 = 1; knot3 = vector(NumberOfKnots3); NumberOfKnots4 = 1; knot4 = vector(NumberOfKnots4); NumberOfKnots5 = 2; knot5 = vector(NumberOfKnots5); NumberOfKnots6 = 3; knot6 = vector(NumberOfKnots6); NumberOfKnots7 = 7; knot7 = vector(NumberOfKnots7); NumberOfKnots8 = 21; knot8 = vector(NumberOfKnots8); NumberOfKnots9 = 49; knot9 = vector(NumberOfKnots9); NumberOfKnots10 = 165; knot10 = vector(NumberOfKnots10); NumberOfKnots11a = 367; knot11a = vector(NumberOfKnots11a); NumberOfKnots11n = 185; knot11n = vector(NumberOfKnots11n); knot3[1] = [1, 4, 2, 5; 3, 6, 4, 1; 5, 2, 6, 3]; knot4[1] = [4, 2, 5, 1; 8, 6, 1, 5; 6, 3, 7, 4; 2, 7, 3, 8]; knot5[1] = [1, 6, 2, 7; 3, 8, 4, 9; 5, 10, 6, 1; 7, 2, 8, 3; 9, 4, 10, 5]; knot5[2] = [1, 4, 2, 5; 3, 8, 4, 9; 5, 10, 6, 1; 9, 6, 10, 7; 7, 2, 8, 3]; knot6[1] = [1, 4, 2, 5; 7, 10, 8, 11; 3, 9, 4, 8; 9, 3, 10, 2; 5, 12, 6, 1; 11, 6, 12, 7]; knot6[2] = [1, 4, 2, 5; 5, 10, 6, 11; 3, 9, 4, 8; 9, 3, 10, 2; 7, 12, 8, 1; 11, 6, 12, 7]; knot6[3] = [4, 2, 5, 1; 8, 4, 9, 3; 12, 9, 1, 10; 10, 5, 11, 6; 6, 11, 7, 12; 2, 8, 3, 7]; knot7[1] = [1, 8, 2, 9; 3, 10, 4, 11; 5, 12, 6, 13; 7, 14, 8, 1; 9, 2, 10, 3; 11, 4, 12, 5; 13, 6, 14, 7]; knot7[2] = [1, 4, 2, 5; 3, 10, 4, 11; 5, 14, 6, 1; 7, 12, 8, 13; 11, 8, 12, 9; 13, 6, 14, 7; 9, 2, 10, 3]; knot7[3] = [6, 2, 7, 1; 10, 4, 11, 3; 14, 8, 1, 7; 8, 14, 9, 13; 12, 6, 13, 5; 2, 10, 3, 9; 4, 12, 5, 11]; knot7[4] = [6, 2, 7, 1; 12, 6, 13, 5; 14, 8, 1, 7; 8, 14, 9, 13; 2, 12, 3, 11; 10, 4, 11, 3; 4, 10, 5, 9]; knot7[5] = [1, 4, 2, 5; 3, 10, 4, 11; 5, 12, 6, 13; 7, 14, 8, 1; 13, 6, 14, 7; 11, 8, 12, 9; 9, 2, 10, 3]; knot7[6] = [1, 4, 2, 5; 3, 8, 4, 9; 5, 12, 6, 13; 9, 1, 10, 14; 13, 11, 14, 10; 11, 6, 12, 7; 7, 2, 8, 3]; knot7[7] = [1, 4, 2, 5; 5, 10, 6, 11; 3, 9, 4, 8; 9, 3, 10, 2; 11, 14, 12, 1; 7, 13, 8, 12; 13, 7, 14, 6]; knot8[1] = [1, 4, 2, 5; 9, 12, 10, 13; 3, 11, 4, 10; 11, 3, 12, 2; 5, 16, 6, 1; 7, 14, 8, 15; 13, 8, 14, 9; 15, 6, 16, 7]; knot8[2] = [1, 4, 2, 5; 5, 12, 6, 13; 3, 11, 4, 10; 11, 3, 12, 2; 7, 14, 8, 15; 9, 16, 10, 1; 13, 6, 14, 7; 15, 8, 16, 9]; knot8[3] = [6, 2, 7, 1; 14, 10, 15, 9; 10, 5, 11, 6; 12, 3, 13, 4; 4, 11, 5, 12; 2, 13, 3, 14; 16, 8, 1, 7; 8, 16, 9, 15]; knot8[4] = [6, 2, 7, 1; 14, 10, 15, 9; 10, 3, 11, 4; 2, 13, 3, 14; 12, 5, 13, 6; 16, 8, 1, 7; 4, 11, 5, 12; 8, 16, 9, 15]; knot8[5] = [6, 2, 7, 1; 8, 4, 9, 3; 2, 8, 3, 7; 14, 10, 15, 9; 12, 5, 13, 6; 4, 13, 5, 14; 16, 12, 1, 11; 10, 16, 11, 15]; knot8[6] = [1, 4, 2, 5; 9, 12, 10, 13; 3, 11, 4, 10; 11, 3, 12, 2; 5, 14, 6, 15; 7, 16, 8, 1; 15, 6, 16, 7; 13, 8, 14, 9]; knot8[7] = [1, 4, 2, 5; 3, 10, 4, 11; 11, 1, 12, 16; 5, 13, 6, 12; 7, 15, 8, 14; 13, 7, 14, 6; 15, 9, 16, 8; 9, 2, 10, 3]; knot8[8] = [1, 4, 2, 5; 3, 8, 4, 9; 11, 15, 12, 14; 5, 13, 6, 12; 13, 7, 14, 6; 9, 1, 10, 16; 15, 11, 16, 10; 7, 2, 8, 3]; knot8[9] = [6, 2, 7, 1; 14, 8, 15, 7; 10, 3, 11, 4; 2, 13, 3, 14; 12, 5, 13, 6; 4, 11, 5, 12; 16, 10, 1, 9; 8, 16, 9, 15]; knot8[10] = [1, 4, 2, 5; 3, 8, 4, 9; 9, 15, 10, 14; 5, 13, 6, 12; 13, 7, 14, 6; 11, 1, 12, 16; 15, 11, 16, 10; 7, 2, 8, 3]; knot8[11] = [1, 4, 2, 5; 5, 12, 6, 13; 3, 11, 4, 10; 11, 3, 12, 2; 9, 16, 10, 1; 15, 6, 16, 7; 7, 14, 8, 15; 13, 8, 14, 9]; knot8[12] = [4, 2, 5, 1; 10, 8, 11, 7; 8, 3, 9, 4; 2, 9, 3, 10; 14, 6, 15, 5; 16, 11, 1, 12; 12, 15, 13, 16; 6, 14, 7, 13]; knot8[13] = [1, 4, 2, 5; 3, 10, 4, 11; 11, 1, 12, 16; 5, 13, 6, 12; 15, 7, 16, 6; 7, 15, 8, 14; 13, 9, 14, 8; 9, 2, 10, 3]; knot8[14] = [1, 4, 2, 5; 5, 10, 6, 11; 3, 9, 4, 8; 9, 3, 10, 2; 7, 14, 8, 15; 11, 16, 12, 1; 15, 12, 16, 13; 13, 6, 14, 7]; knot8[15] = [1, 4, 2, 5; 3, 8, 4, 9; 5, 12, 6, 13; 13, 16, 14, 1; 9, 14, 10, 15; 15, 10, 16, 11; 11, 6, 12, 7; 7, 2, 8, 3]; knot8[16] = [6, 2, 7, 1; 14, 6, 15, 5; 16, 11, 1, 12; 12, 7, 13, 8; 8, 3, 9, 4; 4, 9, 5, 10; 10, 15, 11, 16; 2, 14, 3, 13]; knot8[17] = [6, 2, 7, 1; 14, 8, 15, 7; 8, 3, 9, 4; 2, 13, 3, 14; 12, 5, 13, 6; 4, 9, 5, 10; 16, 12, 1, 11; 10, 16, 11, 15]; knot8[18] = [6, 2, 7, 1; 8, 3, 9, 4; 16, 11, 1, 12; 2, 14, 3, 13; 4, 15, 5, 16; 10, 6, 11, 5; 12, 7, 13, 8; 14, 10, 15, 9]; knot8[19] = [4, 2, 5, 1; 8, 4, 9, 3; 9, 15, 10, 14; 5, 13, 6, 12; 13, 7, 14, 6; 11, 1, 12, 16; 15, 11, 16, 10; 2, 8, 3, 7]; knot8[20] = [4, 2, 5, 1; 8, 4, 9, 3; 5, 12, 6, 13; 13, 16, 14, 1; 9, 14, 10, 15; 15, 10, 16, 11; 11, 6, 12, 7; 2, 8, 3, 7]; knot8[21] = [1, 4, 2, 5; 3, 8, 4, 9; 12, 6, 13, 5; 13, 16, 14, 1; 9, 14, 10, 15; 15, 10, 16, 11; 6, 12, 7, 11; 7, 2, 8, 3]; knot9[1] = [1, 10, 2, 11; 3, 12, 4, 13; 5, 14, 6, 15; 7, 16, 8, 17; 9, 18, 10, 1; 11, 2, 12, 3; 13, 4, 14, 5; 15, 6, 16, 7; 17, 8, 18, 9]; knot9[2] = [1, 4, 2, 5; 3, 12, 4, 13; 5, 18, 6, 1; 7, 16, 8, 17; 9, 14, 10, 15; 13, 10, 14, 11; 15, 8, 16, 9; 17, 6, 18, 7; 11, 2, 12, 3]; knot9[3] = [8, 2, 9, 1; 12, 4, 13, 3; 18, 10, 1, 9; 10, 18, 11, 17; 14, 6, 15, 5; 16, 8, 17, 7; 2, 12, 3, 11; 4, 14, 5, 13; 6, 16, 7, 15]; knot9[4] = [1, 6, 2, 7; 3, 12, 4, 13; 7, 18, 8, 1; 9, 16, 10, 17; 15, 10, 16, 11; 17, 8, 18, 9; 5, 14, 6, 15; 11, 2, 12, 3; 13, 4, 14, 5]; knot9[5] = [6, 2, 7, 1; 14, 6, 15, 5; 18, 8, 1, 7; 16, 10, 17, 9; 10, 16, 11, 15; 8, 18, 9, 17; 2, 14, 3, 13; 12, 4, 13, 3; 4, 12, 5, 11]; knot9[6] = [1, 4, 2, 5; 3, 12, 4, 13; 5, 14, 6, 15; 7, 16, 8, 17; 9, 18, 10, 1; 15, 6, 16, 7; 17, 8, 18, 9; 13, 10, 14, 11; 11, 2, 12, 3]; knot9[7] = [1, 4, 2, 5; 3, 12, 4, 13; 5, 16, 6, 17; 7, 18, 8, 1; 17, 6, 18, 7; 9, 14, 10, 15; 13, 10, 14, 11; 15, 8, 16, 9; 11, 2, 12, 3]; knot9[8] = [1, 4, 2, 5; 3, 8, 4, 9; 5, 14, 6, 15; 9, 1, 10, 18; 11, 17, 12, 16; 15, 13, 16, 12; 17, 11, 18, 10; 13, 6, 14, 7; 7, 2, 8, 3]; knot9[9] = [1, 6, 2, 7; 3, 12, 4, 13; 7, 16, 8, 17; 9, 18, 10, 1; 17, 8, 18, 9; 15, 10, 16, 11; 5, 14, 6, 15; 11, 2, 12, 3; 13, 4, 14, 5]; knot9[10] = [8, 2, 9, 1; 12, 4, 13, 3; 18, 10, 1, 9; 10, 18, 11, 17; 16, 8, 17, 7; 2, 12, 3, 11; 4, 16, 5, 15; 14, 6, 15, 5; 6, 14, 7, 13]; knot9[11] = [1, 4, 2, 5; 9, 12, 10, 13; 3, 11, 4, 10; 11, 3, 12, 2; 13, 1, 14, 18; 5, 15, 6, 14; 7, 17, 8, 16; 15, 7, 16, 6; 17, 9, 18, 8]; knot9[12] = [1, 4, 2, 5; 3, 10, 4, 11; 5, 16, 6, 17; 11, 1, 12, 18; 17, 13, 18, 12; 7, 14, 8, 15; 13, 8, 14, 9; 15, 6, 16, 7; 9, 2, 10, 3]; knot9[13] = [6, 2, 7, 1; 14, 6, 15, 5; 16, 8, 17, 7; 18, 10, 1, 9; 8, 18, 9, 17; 10, 16, 11, 15; 2, 14, 3, 13; 12, 4, 13, 3; 4, 12, 5, 11]; knot9[14] = [1, 4, 2, 5; 5, 12, 6, 13; 3, 11, 4, 10; 11, 3, 12, 2; 13, 18, 14, 1; 9, 15, 10, 14; 7, 17, 8, 16; 15, 9, 16, 8; 17, 7, 18, 6]; knot9[15] = [1, 4, 2, 5; 7, 10, 8, 11; 3, 9, 4, 8; 9, 3, 10, 2; 13, 17, 14, 16; 5, 15, 6, 14; 15, 7, 16, 6; 11, 1, 12, 18; 17, 13, 18, 12]; knot9[16] = [4, 2, 5, 1; 12, 4, 13, 3; 16, 6, 17, 5; 18, 8, 1, 7; 6, 18, 7, 17; 10, 16, 11, 15; 14, 10, 15, 9; 8, 14, 9, 13; 2, 12, 3, 11]; knot9[17] = [1, 4, 2, 5; 5, 12, 6, 13; 3, 11, 4, 10; 11, 3, 12, 2; 7, 14, 8, 15; 13, 6, 14, 7; 15, 18, 16, 1; 9, 17, 10, 16; 17, 9, 18, 8]; knot9[18] = [1, 4, 2, 5; 3, 12, 4, 13; 5, 14, 6, 15; 9, 18, 10, 1; 17, 6, 18, 7; 7, 16, 8, 17; 15, 8, 16, 9; 13, 10, 14, 11; 11, 2, 12, 3]; knot9[19] = [1, 4, 2, 5; 5, 10, 6, 11; 3, 9, 4, 8; 9, 3, 10, 2; 13, 16, 14, 17; 7, 15, 8, 14; 15, 7, 16, 6; 11, 18, 12, 1; 17, 12, 18, 13]; knot9[20] = [1, 4, 2, 5; 3, 10, 4, 11; 5, 14, 6, 15; 7, 16, 8, 17; 11, 1, 12, 18; 15, 6, 16, 7; 17, 13, 18, 12; 13, 8, 14, 9; 9, 2, 10, 3]; knot9[21] = [1, 4, 2, 5; 9, 12, 10, 13; 3, 11, 4, 10; 11, 3, 12, 2; 13, 1, 14, 18; 5, 15, 6, 14; 17, 7, 18, 6; 7, 17, 8, 16; 15, 9, 16, 8]; knot9[22] = [4, 2, 5, 1; 10, 6, 11, 5; 8, 3, 9, 4; 2, 9, 3, 10; 16, 12, 17, 11; 14, 7, 15, 8; 6, 15, 7, 16; 18, 14, 1, 13; 12, 18, 13, 17]; knot9[23] = [1, 4, 2, 5; 3, 10, 4, 11; 5, 12, 6, 13; 7, 16, 8, 17; 13, 18, 14, 1; 17, 14, 18, 15; 15, 6, 16, 7; 11, 8, 12, 9; 9, 2, 10, 3]; knot9[24] = [1, 4, 2, 5; 3, 8, 4, 9; 5, 14, 6, 15; 9, 17, 10, 16; 11, 1, 12, 18; 17, 11, 18, 10; 15, 13, 16, 12; 13, 6, 14, 7; 7, 2, 8, 3]; knot9[25] = [1, 4, 2, 5; 3, 8, 4, 9; 5, 12, 6, 13; 9, 17, 10, 16; 13, 18, 14, 1; 17, 14, 18, 15; 15, 11, 16, 10; 11, 6, 12, 7; 7, 2, 8, 3]; knot9[26] = [1, 4, 2, 5; 5, 12, 6, 13; 3, 11, 4, 10; 11, 3, 12, 2; 13, 18, 14, 1; 7, 15, 8, 14; 17, 7, 18, 6; 9, 17, 10, 16; 15, 9, 16, 8]; knot9[27] = [1, 4, 2, 5; 3, 10, 4, 11; 11, 1, 12, 18; 5, 13, 6, 12; 13, 17, 14, 16; 7, 14, 8, 15; 15, 6, 16, 7; 17, 9, 18, 8; 9, 2, 10, 3]; knot9[28] = [1, 4, 2, 5; 3, 8, 4, 9; 11, 15, 12, 14; 5, 13, 6, 12; 13, 7, 14, 6; 15, 18, 16, 1; 9, 16, 10, 17; 17, 10, 18, 11; 7, 2, 8, 3]; knot9[29] = [6, 2, 7, 1; 16, 11, 17, 12; 10, 4, 11, 3; 2, 15, 3, 16; 14, 5, 15, 6; 18, 8, 1, 7; 4, 10, 5, 9; 12, 17, 13, 18; 8, 13, 9, 14]; knot9[30] = [4, 2, 5, 1; 10, 6, 11, 5; 8, 3, 9, 4; 2, 9, 3, 10; 14, 8, 15, 7; 18, 15, 1, 16; 16, 11, 17, 12; 12, 17, 13, 18; 6, 14, 7, 13]; knot9[31] = [1, 4, 2, 5; 3, 10, 4, 11; 11, 1, 12, 18; 5, 13, 6, 12; 17, 7, 18, 6; 7, 14, 8, 15; 13, 16, 14, 17; 15, 8, 16, 9; 9, 2, 10, 3]; knot9[32] = [1, 4, 2, 5; 13, 18, 14, 1; 3, 9, 4, 8; 9, 3, 10, 2; 7, 15, 8, 14; 15, 11, 16, 10; 5, 12, 6, 13; 11, 17, 12, 16; 17, 7, 18, 6]; knot9[33] = [4, 2, 5, 1; 12, 8, 13, 7; 8, 3, 9, 4; 2, 9, 3, 10; 18, 13, 1, 14; 14, 5, 15, 6; 6, 17, 7, 18; 16, 12, 17, 11; 10, 16, 11, 15]; knot9[34] = [6, 2, 7, 1; 16, 8, 17, 7; 8, 3, 9, 4; 2, 15, 3, 16; 14, 9, 15, 10; 10, 6, 11, 5; 4, 14, 5, 13; 18, 11, 1, 12; 12, 17, 13, 18]; knot9[35] = [1, 8, 2, 9; 7, 14, 8, 15; 5, 16, 6, 17; 9, 18, 10, 1; 15, 6, 16, 7; 17, 10, 18, 11; 13, 2, 14, 3; 3, 12, 4, 13; 11, 4, 12, 5]; knot9[36] = [1, 4, 2, 5; 7, 10, 8, 11; 3, 9, 4, 8; 9, 3, 10, 2; 11, 17, 12, 16; 5, 15, 6, 14; 15, 7, 16, 6; 13, 1, 14, 18; 17, 13, 18, 12]; knot9[37] = [1, 4, 2, 5; 7, 12, 8, 13; 3, 11, 4, 10; 11, 3, 12, 2; 5, 14, 6, 15; 13, 6, 14, 7; 15, 18, 16, 1; 9, 17, 10, 16; 17, 9, 18, 8]; knot9[38] = [1, 6, 2, 7; 5, 14, 6, 15; 7, 18, 8, 1; 15, 8, 16, 9; 3, 10, 4, 11; 9, 4, 10, 5; 17, 12, 18, 13; 11, 16, 12, 17; 13, 2, 14, 3]; knot9[39] = [1, 6, 2, 7; 3, 11, 4, 10; 7, 18, 8, 1; 17, 13, 18, 12; 9, 17, 10, 16; 5, 15, 6, 14; 15, 5, 16, 4; 11, 3, 12, 2; 13, 9, 14, 8]; knot9[40] = [1, 6, 2, 7; 7, 12, 8, 13; 5, 15, 6, 14; 11, 3, 12, 2; 15, 10, 16, 11; 3, 16, 4, 17; 9, 4, 10, 5; 17, 9, 18, 8; 13, 18, 14, 1]; knot9[41] = [6, 2, 7, 1; 12, 8, 13, 7; 14, 5, 15, 6; 10, 3, 11, 4; 2, 11, 3, 12; 4, 15, 5, 16; 8, 17, 9, 18; 16, 9, 17, 10; 18, 14, 1, 13]; knot9[42] = [1, 4, 2, 5; 5, 10, 6, 11; 3, 9, 4, 8; 9, 3, 10, 2; 16, 12, 17, 11; 14, 7, 15, 8; 6, 15, 7, 16; 18, 14, 1, 13; 12, 18, 13, 17]; knot9[43] = [4, 2, 5, 1; 10, 6, 11, 5; 8, 3, 9, 4; 2, 9, 3, 10; 14, 8, 15, 7; 15, 1, 16, 18; 11, 17, 12, 16; 17, 13, 18, 12; 6, 14, 7, 13]; knot9[44] = [1, 4, 2, 5; 5, 10, 6, 11; 3, 9, 4, 8; 9, 3, 10, 2; 14, 8, 15, 7; 18, 15, 1, 16; 16, 11, 17, 12; 12, 17, 13, 18; 6, 14, 7, 13]; knot9[45] = [4, 2, 5, 1; 10, 6, 11, 5; 8, 3, 9, 4; 2, 9, 3, 10; 7, 14, 8, 15; 18, 15, 1, 16; 16, 11, 17, 12; 12, 17, 13, 18; 13, 6, 14, 7]; knot9[46] = [4, 2, 5, 1; 7, 12, 8, 13; 10, 3, 11, 4; 2, 11, 3, 12; 5, 14, 6, 15; 13, 6, 14, 7; 15, 18, 16, 1; 9, 17, 10, 16; 17, 9, 18, 8]; knot9[47] = [6, 2, 7, 1; 16, 8, 17, 7; 8, 3, 9, 4; 2, 15, 3, 16; 14, 9, 15, 10; 10, 6, 11, 5; 4, 14, 5, 13; 11, 1, 12, 18; 17, 13, 18, 12]; knot9[48] = [1, 4, 2, 5; 12, 8, 13, 7; 3, 11, 4, 10; 11, 3, 12, 2; 14, 6, 15, 5; 6, 14, 7, 13; 15, 18, 16, 1; 9, 17, 10, 16; 17, 9, 18, 8]; knot9[49] = [6, 2, 7, 1; 12, 8, 13, 7; 5, 15, 6, 14; 3, 11, 4, 10; 11, 3, 12, 2; 15, 5, 16, 4; 17, 9, 18, 8; 9, 17, 10, 16; 18, 14, 1, 13]; knot10[1] = [1, 4, 2, 5; 11, 14, 12, 15; 3, 13, 4, 12; 13, 3, 14, 2; 5, 20, 6, 1; 7, 18, 8, 19; 9, 16, 10, 17; 15, 10, 16, 11; 17, 8, 18, 9; 19, 6, 20, 7]; knot10[2] = [1, 4, 2, 5; 5, 14, 6, 15; 3, 13, 4, 12; 13, 3, 14, 2; 7, 16, 8, 17; 9, 18, 10, 19; 11, 20, 12, 1; 15, 6, 16, 7; 17, 8, 18, 9; 19, 10, 20, 11]; knot10[3] = [1, 6, 2, 7; 11, 16, 12, 17; 5, 13, 6, 12; 3, 15, 4, 14; 13, 5, 14, 4; 15, 3, 16, 2; 7, 20, 8, 1; 9, 18, 10, 19; 17, 10, 18, 11; 19, 8, 20, 9]; knot10[4] = [1, 6, 2, 7; 11, 16, 12, 17; 3, 13, 4, 12; 15, 3, 16, 2; 5, 15, 6, 14; 7, 20, 8, 1; 9, 18, 10, 19; 13, 5, 14, 4; 17, 10, 18, 11; 19, 8, 20, 9]; knot10[5] = [1, 4, 2, 5; 3, 12, 4, 13; 13, 1, 14, 20; 5, 15, 6, 14; 7, 17, 8, 16; 9, 19, 10, 18; 15, 7, 16, 6; 17, 9, 18, 8; 19, 11, 20, 10; 11, 2, 12, 3]; knot10[6] = [1, 4, 2, 5; 11, 14, 12, 15; 3, 13, 4, 12; 13, 3, 14, 2; 5, 16, 6, 17; 7, 18, 8, 19; 9, 20, 10, 1; 17, 6, 18, 7; 19, 8, 20, 9; 15, 10, 16, 11]; knot10[7] = [1, 4, 2, 5; 5, 14, 6, 15; 3, 13, 4, 12; 13, 3, 14, 2; 11, 20, 12, 1; 19, 6, 20, 7; 7, 18, 8, 19; 9, 16, 10, 17; 15, 10, 16, 11; 17, 8, 18, 9]; knot10[8] = [1, 6, 2, 7; 7, 16, 8, 17; 5, 13, 6, 12; 3, 15, 4, 14; 13, 5, 14, 4; 15, 3, 16, 2; 9, 18, 10, 19; 11, 20, 12, 1; 17, 8, 18, 9; 19, 10, 20, 11]; knot10[9] = [6, 2, 7, 1; 16, 8, 17, 7; 12, 3, 13, 4; 2, 15, 3, 16; 14, 5, 15, 6; 4, 13, 5, 14; 18, 10, 19, 9; 20, 12, 1, 11; 8, 18, 9, 17; 10, 20, 11, 19]; knot10[10] = [1, 4, 2, 5; 3, 12, 4, 13; 13, 1, 14, 20; 5, 15, 6, 14; 19, 7, 20, 6; 7, 19, 8, 18; 9, 17, 10, 16; 15, 11, 16, 10; 17, 9, 18, 8; 11, 2, 12, 3]; knot10[11] = [1, 6, 2, 7; 11, 16, 12, 17; 5, 13, 6, 12; 3, 15, 4, 14; 13, 5, 14, 4; 15, 3, 16, 2; 7, 18, 8, 19; 9, 20, 10, 1; 19, 8, 20, 9; 17, 10, 18, 11]; knot10[12] = [1, 4, 2, 5; 3, 10, 4, 11; 13, 19, 14, 18; 5, 15, 6, 14; 7, 17, 8, 16; 15, 7, 16, 6; 17, 9, 18, 8; 11, 1, 12, 20; 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