Diagrams of 8_18: Go
| name: | 8_18 |
| category: | 8 |
| alternating: | Y |
| name_rank: | 33 |
| dt_name: | 8a_12 |
| dt_rank: | 27 |
| dt_notation: | [6, 8, 10, 12, 14, 16, 2, 4] |
| classical_conway_name: | 8_18 |
| conway_notation: | [8*] |
| two_bridge_notation: | NULL |
| fibered: | Y |
| gauss_notation: | [-1, 2, -3, 4, -5, 1, -6, 3, -7, 5, -8, 6, -2, 7, -4, 8] |
| pd_notation: | [[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]] |
| crossing_number: | 8 |
| tetrahedral_census_name: | [[10, 13], hyperbolic, not in census] |
| unknotting_number: | 2 |
| three_genus: | 3 |
| crosscap_number: | 4 |
| bridge_index: | 3 |
| braid_index: | 3 |
| braid_length: | 8 |
| braid_notation: | [1,-2,1,-2,1,-2,1,-2] |
| signature: | 0 |
| nakanishi_index: | 2 |
| super_bridge_index: | 4 |
| thurston_bennequin_number: | [-5][-5] |
| arc_index: | 10 |
| polygon_index: | 9 |
| tunnel_number: | 2 |
| morse_novikov_number: | 0 |
| alexander_polynomial: | 1-5*t+ 10*t^2-13*t^3+ 10*t^4-5*t^5+ t^6 |
| alexander_polynomial_vector: | [0, 6, 1, -5, 10, -13, 10, -5, 1] |
| jones_polynomial: | t^(-4)-4*t^(-3)+ 6*t^(-2)-7*t^(-1)+ 9-7*t+ 6*t^2-4*t^3+ t^4 |
| jones_polynomial_vector: | [-4, 4, 1, -4, 6, -7, 9, -7, 6, -4, 1] |
| conway_polynomial: | 1+ z^2-z^4-z^6 |
| conway_polynomial_vector: | [0, 3, 1, 1, -1, -1] |
| kauffman_polynomial: | (a^(-2)+ 3+ a^2)*z^(0)+ (a^(-1)+ a)*z^(1)+ (3*a^(-2)+ 6+ 3*a^2)*z^(2)+ (-4*a^(-3)-9*a^(-1)-9*a-4*a^3)*z^(3)+ (a^(-4)-9*a^(-2)-20-9*a^2+ a^4)*z^(4)+ (4*a^(-3)+ 3*a^(-1)+ 3*a+ 4*a^3)*z^(5)+ (6*a^(-2)+ 12+ 6*a^2)*z^(6)+ (3*a^(-1)+ 3*a)*z^(7) |
| kauffman_polynomial_vector: | [0, 7, [-2, 2, 1, 0, 3, 0, 1], [-1, 1, 1, 0, 1], [-2, 2, 3, 0, 6, 0, 3], [-3, 3, -4, 0, -9, 0, -9, 0, -4], [-4, 4, 1, 0, -9, 0, -20, 0, -9, 0, 1], [-3, 3, 4, 0, 3, 0, 3, 0, 4], [-2, 2, 6, 0, 12, 0, 6], [-1, 1, 3, 0, 3]] |
| a_polynomial: | table of A-polys |
| smooth_four_genus: | 1 |
| topological_four_genus: | 1 |
| smooth_4d_crosscap_number: | 3 |
| topological_4d_crosscap_number: | NULL |
| smooth_concordance_genus: | 3 |
| topological_concordance_genus: | NULL |
| smooth_concordance_crosscap_number: | NULL |
| topological_concordance_crosscap_number: | NULL |
| algebraic_concordance_order: | 2 |
| smooth_concordance_order: | 2 |
| topological_concordance_order: | 2 |
| ribbon: | NULL |
| determinant: | 45 |
| seifert_matrix: | [[ 1, 0, 0, 0, -1, 0], [ 0, -1, 0, 0, 0, 0], [ 0, -1, -1, 0, 0, 0], [ 1, -1, -1, 1, -1, 1], [ 0, -1, -1, 0, -1, 0], [ 1, 0, -1, 0, -1, 1]] |
| rasmussen_invariant: | 0 |
| ozsvath_szabo_tau_invariant: | 0 |
| volume: | 12.3509062091 |
| maximum_cusp_volume: | 9.447477653 |
| longitude_translation: | (12.16068464, 0) |
| meridian_translation: | (0, 1.553773974) |
| longitude_length: | 12.16068464 |
| meridian_length: | 1.553773974 |
| other_short_geodesics: | NULL |
| symmetry_type: | fully amphicheiral |
| full_symmetry_group: | D8 |
| chern_simons_invariant: | 0 |
| volume_imaginary_part: | 0 |
| arf_invariant: | 1 |
| turaev_genus: | 0 |
| signature_function: | [[0.3333333333, [0, 0, 0], 2]] |
| monodromy: | abAcBdEDCHcd |
| small_large: | Small |
| positive_braid: | N |
| positive: | N |
| strongly_quasipositive: | N |
| quasipositive: | N |
| positive_braid_notation: | does not exist |
| positive_pd_notation: | does not exist |
| strongly_quasipositive_braid_notation: | does not exist |
| quasipositive_braid_notation: | does not exist |
| fd_clasp_number: | 2 |
| width: | 18 |
| torsion_numbers: | [[2,[3,15]], [3,[2,2,8,8]], [4,[3,3,3,15]], [5,[11,11]], [6,[4,20,0,0,0,0]], [7,[29,29]], [8,[3,3,21,105]], [9,[2,2,152,152]]] |
| td_clasp_number: | 3 |
| l_space: | No |
| nu: | [0,0] |
| epsilon: | 0 |
| quasi_alternating: | Y |
| almost_alternating: | N |
| adequate: | Y |
| montesinos_notation: | Not Montesinos |
| boundary_slopes: | Not Montesinos |
| pretzel_notation: | Non-pretzel |
| double_slice_genus: | 2 |
| unknotting_number_algebraic: | 2 |
| khovanov_unreduced_integral_polynomial: | t^(-4)*q^(-9)+ 3*t^(-3)*q^(-7)+ t^(-3)*q^(-5)+ 3*t^(-2)*q^(-5)+ 3*t^(-2)*q^(-3)+ 4*t^(-1)*q^(-3)+ 3*t^(-1)*q^(-1)+ 5*q^(-1)+ 5*q+ 3*t*q+ 4*t*q^(3)+ 3*t^(2)*q^(3)+ 3*t^(2)*q^(5)+ t^(3)*q^(5)+ 3*t^(3)*q^(7)+ t^(4)*q^(9)+ t^(-3)*q^(-7)*T^(2)+ 3*t^(-2)*q^(-5)*T^(2)+ 3*t^(-1)*q^(-3)*T^(2)+ 4*q^(-1)*T^(2)+ 4*t*q*T^(2)+ 3*t^(2)*q^(3)*T^(2)+ 3*t^(3)*q^(5)*T^(2)+ t^(4)*q^(7)*T^(2) |
| khovanov_unreduced_integral_vector: | [[0, 1, -4, -9], [0, 3, -3, -7], [0, 1, -3, -5], [0, 3, -2, -5], [0, 3, -2, -3], [0, 4, -1, -3], [0, 3, -1, -1], [0, 5, 0, -1], [0, 5, 0, 1], [0, 3, 1, 1], [0, 4, 1, 3], [0, 3, 2, 3], [0, 3, 2, 5], [0, 1, 3, 5], [0, 3, 3, 7], [0, 1, 4, 9], [2, 1, -3, -7], [2, 3, -2, -5], [2, 3, -1, -3], [2, 4, 0, -1], [2, 4, 1, 1], [2, 3, 2, 3], [2, 3, 3, 5], [2, 1, 4, 7]] |
| khovanov_reduced_integral_polynomial: | t^(-4)*q^(-8)+ 4*t^(-3)*q^(-6)+ 6*t^(-2)*q^(-4)+ 7*t^(-1)*q^(-2)+ 9+ 7*t*q^(2)+ 6*t^(2)*q^(4)+ 4*t^(3)*q^(6)+ t^(4)*q^(8) |
| khovanov_reduced_integral_vector: | [[0, 1, -4, -8], [0, 4, -3, -6], [0, 6, -2, -4], [0, 7, -1, -2], [0, 9, 0, 0], [0, 7, 1, 2], [0, 6, 2, 4], [0, 4, 3, 6], [0, 1, 4, 8]] |
| khovanov_reduced_rational_polynomial: | t^(-4)*q^(-8)+ 4*t^(-3)*q^(-6)+ 6*t^(-2)*q^(-4)+ 7*t^(-1)*q^(-2)+ 9+ 7*t*q^(2)+ 6*t^(2)*q^(4)+ 4*t^(3)*q^(6)+ t^(4)*q^(8) |
| khovanov_reduced_rational_vector: | [[1, 1, -4, -8], [1, 4, -3, -6], [1, 6, -2, -4], [1, 7, -1, -2], [1, 9, 0, 0], [1, 7, 1, 2], [1, 6, 2, 4], [1, 4, 3, 6], [1, 1, 4, 8]] |
| khovanov_reduced_mod2_polynomial: | t^(-4)*q^(-8)+ 4*t^(-3)*q^(-6)+ 6*t^(-2)*q^(-4)+ 7*t^(-1)*q^(-2)+ 9+ 7*t*q^(2)+ 6*t^(2)*q^(4)+ 4*t^(3)*q^(6)+ t^(4)*q^(8) |
| khovanov_reduced_mod2_vector: | [[2, 1, -4, -8], [2, 4, -3, -6], [2, 6, -2, -4], [2, 7, -1, -2], [2, 9, 0, 0], [2, 7, 1, 2], [2, 6, 2, 4], [2, 4, 3, 6], [2, 1, 4, 8]] |
| khovanov_odd_integral_polynomial: | t^(-4)*q^(-8)+ 4*t^(-3)*q^(-6)+ 6*t^(-2)*q^(-4)+ 7*t^(-1)*q^(-2)+ 9+ 7*t*q^(2)+ 6*t^(2)*q^(4)+ 4*t^(3)*q^(6)+ t^(4)*q^(8) |
| khovanov_odd_integral_vector: | [[0, 1, -4, -8], [0, 4, -3, -6], [0, 6, -2, -4], [0, 7, -1, -2], [0, 9, 0, 0], [0, 7, 1, 2], [0, 6, 2, 4], [0, 4, 3, 6], [0, 1, 4, 8]] |
| khovanov_odd_mod2_polynomial: | t^(-4)*q^(-8)+ 4*t^(-3)*q^(-6)+ 6*t^(-2)*q^(-4)+ 7*t^(-1)*q^(-2)+ 9+ 7*t*q^(2)+ 6*t^(2)*q^(4)+ 4*t^(3)*q^(6)+ t^(4)*q^(8) |
| khovanov_odd_mod2_vector: | [[2, 1, -4, -8], [2, 4, -3, -6], [2, 6, -2, -4], [2, 7, -1, -2], [2, 9, 0, 0], [2, 7, 1, 2], [2, 6, 2, 4], [2, 4, 3, 6], [2, 1, 4, 8]] |
| khovanov_odd_rational_polynomial: | t^(-4)*q^(-8)+ 4*t^(-3)*q^(-6)+ 6*t^(-2)*q^(-4)+ 7*t^(-1)*q^(-2)+ 9+ 7*t*q^(2)+ 6*t^(2)*q^(4)+ 4*t^(3)*q^(6)+ t^(4)*q^(8) |
| khovanov_odd_rational_vector: | [[1, 1, -4, -8], [1, 4, -3, -6], [1, 6, -2, -4], [1, 7, -1, -2], [1, 9, 0, 0], [1, 7, 1, 2], [1, 6, 2, 4], [1, 4, 3, 6], [1, 1, 4, 8]] |
| hfk_polynomial: | m^(-3)*a^(-3)+ 5*m^(-2)*a^(-2)+ 10*m^(-1)*a^(-1)+ 13+ 10*m*a+ 5*m^2*a^2+ m^3*a^3 |
| hfk_polynomial_vector: | [1,-3,-3;5,-2,-2;10,-1,-1;13,0,0;10,1,1;5,2,2;1,3,3] |
| mosaic_tile_number: | [ 6 , 24 ] |
| ropelength: | 74.9063 |
| homfly_polynomial: | (-v^(-2)+ 3-v^2)+ (v^(-2)-1+ v^2)*z^2+ (v^(-2)-3+ v^2)*z^4-z^6 |
| homfly_polynomial_vector: | [0, 3, [-1, 1, -1, 3, -1], [-1, 1, 1, -1, 1], [-1, 1, 1, -3, 1], [0, 0, -1]] |
| grid_notation: | [[1,1],[1,3],[2,2],[2,5],[3,4],[3,7],[4,5],[4,9],[5,3],[5,8],[6,6],[6,10],[7,1],[7,9],[8,7],[8,10],[9,4],[9,8],[10,2],[10,6]] |
| almost_strongly_qp: | N |
| almost_strongly_qp_braid: | NULL |
| ribbon_number: | D.N.E. |
| geometric_type: | hyperbolic |
| cosmetic_crossing: | N |
![[[0.3333333333, [0, 0, 0], 2]]](sign-func-graphs/siggraph32.png){kind=link}