| Min(phi) over symmetries of the knot is: [-3,-1,-1,1,2,2,0,1,1,2,2,0,1,1,1,1,2,2,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.872'] |
| Arrow polynomial of the knot is: -2*K1*K2 - 4*K1*K3 + K1 + 2*K2 + K3 + 2*K4 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.126', '6.195', '6.367', '6.438', '6.869', '6.872', '6.896', '6.1147'] |
| Outer characteristic polynomial of the knot is: t^7+72t^5+59t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.872'] |
| 2-strand cable arrow polynomial of the knot is: 120*K1**2*K2 - 2752*K1**2*K3**2 - 112*K1**2*K6**2 - 1580*K1**2 + 3976*K1*K2*K3 + 2176*K1*K3*K4 + 40*K1*K4*K5 + 136*K1*K5*K6 + 88*K1*K6*K7 - 1264*K2**2*K3**2 - 8*K2**2*K4**2 + 144*K2**2*K4 - 48*K2**2*K6**2 - 1334*K2**2 + 872*K2*K3*K5 + 72*K2*K4*K6 + 8*K2*K5*K7 + 32*K2*K6*K8 - 1504*K3**2 - 512*K4**2 - 184*K5**2 - 82*K6**2 - 20*K7**2 - 4*K8**2 + 1738 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.872'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16991', 'vk6.17232', 'vk6.20211', 'vk6.21497', 'vk6.23397', 'vk6.23704', 'vk6.27401', 'vk6.29020', 'vk6.35458', 'vk6.35898', 'vk6.38819', 'vk6.41004', 'vk6.42894', 'vk6.43193', 'vk6.45578', 'vk6.47350', 'vk6.55160', 'vk6.55405', 'vk6.57047', 'vk6.58149', 'vk6.59540', 'vk6.59881', 'vk6.61549', 'vk6.62728', 'vk6.64970', 'vk6.65175', 'vk6.66667', 'vk6.67499', 'vk6.68262', 'vk6.68416', 'vk6.69315', 'vk6.70073'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is c. |
| The reverse -K is |
| The mirror image K* is |
| The reversed mirror image -K* is |
| The fillings (up to the first 10) associated to the algebraic genus: |
| Or click here to check the fillings |
| invariant | value |
|---|---|
| Gauss code | O1O2O3O4U1U5O6O5U3U2U4U6 |
| R3 orbit | {'O1O2O3O4U1U5O6O5U3U2U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U1U3U2O6O5U6U4 |
| Gauss code of K* | O1O2O3O4U5U2U1U3O5O6U4U6 |
| Gauss code of -K* | O1O2O3O4U5U1O5O6U2U4U3U6 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 -1 -1 2 1 2],[ 3 0 2 1 3 3 3],[ 1 -2 0 0 2 1 2],[ 1 -1 0 0 1 1 1],[-2 -3 -2 -1 0 -2 0],[-1 -3 -1 -1 2 0 2],[-2 -3 -2 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 2 1 -1 -1 -3],[-2 0 0 -2 -1 -2 -3],[-2 0 0 -2 -1 -2 -3],[-1 2 2 0 -1 -1 -3],[ 1 1 1 1 0 0 -1],[ 1 2 2 1 0 0 -2],[ 3 3 3 3 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,1,1,3,0,2,1,2,3,2,1,2,3,1,1,3,0,1,2] |
| Phi over symmetry | [-3,-1,-1,1,2,2,0,1,1,2,2,0,1,1,1,1,2,2,-1,-1,0] |
| Phi of -K | [-3,-1,-1,1,2,2,0,1,1,2,2,0,1,1,1,1,2,2,-1,-1,0] |
| Phi of K* | [-2,-2,-1,1,1,3,0,-1,1,2,2,-1,1,2,2,1,1,1,0,0,1] |
| Phi of -K* | [-3,-1,-1,1,2,2,1,2,3,3,3,0,1,1,1,1,2,2,2,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-2t^2+t |
| Normalized Jones-Krushkal polynomial | 9z+19 |
| Enhanced Jones-Krushkal polynomial | 4w^4z-8w^3z+13w^2z+19w |
| Inner characteristic polynomial | t^6+52t^4+13t^2 |
| Outer characteristic polynomial | t^7+72t^5+59t^3 |
| Flat arrow polynomial | -2*K1*K2 - 4*K1*K3 + K1 + 2*K2 + K3 + 2*K4 + 1 |
| 2-strand cable arrow polynomial | 120*K1**2*K2 - 2752*K1**2*K3**2 - 112*K1**2*K6**2 - 1580*K1**2 + 3976*K1*K2*K3 + 2176*K1*K3*K4 + 40*K1*K4*K5 + 136*K1*K5*K6 + 88*K1*K6*K7 - 1264*K2**2*K3**2 - 8*K2**2*K4**2 + 144*K2**2*K4 - 48*K2**2*K6**2 - 1334*K2**2 + 872*K2*K3*K5 + 72*K2*K4*K6 + 8*K2*K5*K7 + 32*K2*K6*K8 - 1504*K3**2 - 512*K4**2 - 184*K5**2 - 82*K6**2 - 20*K7**2 - 4*K8**2 + 1738 |
| Genus of based matrix | 2 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{1, 6}, {5}, {2, 4}, {3}], [{1, 6}, {5}, {3, 4}, {2}], [{1, 6}, {5}, {4}, {2, 3}], [{1, 6}, {5}, {4}, {3}, {2}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{2, 6}, {5}, {1, 4}, {3}], [{2, 6}, {5}, {3, 4}, {1}], [{2, 6}, {5}, {4}, {1, 3}], [{2, 6}, {5}, {4}, {3}, {1}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}], [{3, 6}, {5}, {1, 4}, {2}], [{3, 6}, {5}, {2, 4}, {1}], [{3, 6}, {5}, {4}, {1, 2}], [{3, 6}, {5}, {4}, {2}, {1}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{4, 6}, {5}, {1, 3}, {2}], [{4, 6}, {5}, {2, 3}, {1}], [{4, 6}, {5}, {3}, {1, 2}], [{4, 6}, {5}, {3}, {2}, {1}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}], [{5, 6}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}], [{5, 6}, {4}, {1, 3}, {2}], [{5, 6}, {4}, {2, 3}, {1}], [{5, 6}, {4}, {3}, {1, 2}], [{5, 6}, {4}, {3}, {2}, {1}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {1, 5}, {4}, {3}, {2}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {2, 5}, {4}, {3}, {1}], [{6}, {3, 5}, {1, 4}, {2}], [{6}, {3, 5}, {2, 4}, {1}], [{6}, {3, 5}, {4}, {1, 2}], [{6}, {3, 5}, {4}, {2}, {1}], [{6}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {4, 5}, {3}, {2}, {1}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {1, 4}, {3}, {2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {3, 4}, {2}, {1}], [{6}, {5}, {4}, {1, 3}, {2}], [{6}, {5}, {4}, {2, 3}, {1}], [{6}, {5}, {4}, {3}, {1, 2}], [{6}, {5}, {4}, {3}, {2}, {1}]] |
| If K is slice | False |