| Min(phi) over symmetries of the knot is: [-3,-3,-1,2,2,3,0,0,1,3,3,0,2,4,4,0,1,1,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.233'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1*K2 - 2*K1 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.233', '6.340', '6.382', '6.550', '6.656', '6.663', '6.683', '6.698', '6.739', '6.745', '6.759', '6.765', '6.1357', '6.1358', '6.1370'] |
| Outer characteristic polynomial of the knot is: t^7+94t^5+115t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.233'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**2*K2**4 + 256*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 1776*K1**2*K2**2 - 64*K1**2*K2*K4 + 2264*K1**2*K2 - 64*K1**2*K4**2 - 1816*K1**2 + 160*K1*K2**3*K3 - 608*K1*K2**2*K3 - 64*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 2160*K1*K2*K3 + 352*K1*K3*K4 + 48*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 480*K2**4 - 240*K2**2*K3**2 - 72*K2**2*K4**2 + 840*K2**2*K4 - 1472*K2**2 + 280*K2*K3*K5 + 64*K2*K4*K6 - 704*K3**2 - 336*K4**2 - 88*K5**2 - 16*K6**2 + 1470 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.233'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17005', 'vk6.17248', 'vk6.17537', 'vk6.17548', 'vk6.17592', 'vk6.17605', 'vk6.21914', 'vk6.24043', 'vk6.24058', 'vk6.24152', 'vk6.27970', 'vk6.29443', 'vk6.35481', 'vk6.35932', 'vk6.36321', 'vk6.36336', 'vk6.36403', 'vk6.39378', 'vk6.41563', 'vk6.43446', 'vk6.43457', 'vk6.43503', 'vk6.45949', 'vk6.47630', 'vk6.55180', 'vk6.55424', 'vk6.55635', 'vk6.55638', 'vk6.55663', 'vk6.58564', 'vk6.60153', 'vk6.60213', 'vk6.62053', 'vk6.63044', 'vk6.64978', 'vk6.65188', 'vk6.65340', 'vk6.65372', 'vk6.68506', 'vk6.68530'] |
| 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 | O1O2O3O4O5U3O6U2U6U1U5U4 |
| R3 orbit | {'O1O2O3O4O5U3U1O6U2U6U5U4', 'O1O2O3O4O5U3O6U2U6U1U5U4'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U2U1U5U6U4O6U3 |
| Gauss code of K* | O1O2O3O4O5U3U1U6U5U4O6U2 |
| Gauss code of -K* | O1O2O3O4O5U4O6U2U1U6U5U3 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 3 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -3 -2 3 3 1],[ 2 0 -1 0 4 3 1],[ 3 1 0 0 4 3 1],[ 2 0 0 0 2 1 0],[-3 -4 -4 -2 0 0 0],[-3 -3 -3 -1 0 0 0],[-1 -1 -1 0 0 0 0]] |
| Primitive based matrix | [[ 0 3 3 1 -2 -2 -3],[-3 0 0 0 -1 -3 -3],[-3 0 0 0 -2 -4 -4],[-1 0 0 0 0 -1 -1],[ 2 1 2 0 0 0 0],[ 2 3 4 1 0 0 -1],[ 3 3 4 1 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-3,-1,2,2,3,0,0,1,3,3,0,2,4,4,0,1,1,0,0,1] |
| Phi over symmetry | [-3,-3,-1,2,2,3,0,0,1,3,3,0,2,4,4,0,1,1,0,0,1] |
| Phi of -K | [-3,-2,-2,1,3,3,0,1,3,2,3,0,2,1,2,3,3,4,2,2,0] |
| Phi of K* | [-3,-3,-1,2,2,3,0,2,1,3,2,2,2,4,3,2,3,3,0,0,1] |
| Phi of -K* | [-3,-2,-2,1,3,3,0,1,1,3,4,0,0,1,2,1,3,4,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+2t^2-t |
| Normalized Jones-Krushkal polynomial | 6z^2+19z+15 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2+19w^2z+15w |
| Inner characteristic polynomial | t^6+58t^4+23t^2 |
| Outer characteristic polynomial | t^7+94t^5+115t^3+3t |
| Flat arrow polynomial | 4*K1**3 - 2*K1*K2 - 2*K1 + 1 |
| 2-strand cable arrow polynomial | -192*K1**2*K2**4 + 256*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 1776*K1**2*K2**2 - 64*K1**2*K2*K4 + 2264*K1**2*K2 - 64*K1**2*K4**2 - 1816*K1**2 + 160*K1*K2**3*K3 - 608*K1*K2**2*K3 - 64*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 2160*K1*K2*K3 + 352*K1*K3*K4 + 48*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 480*K2**4 - 240*K2**2*K3**2 - 72*K2**2*K4**2 + 840*K2**2*K4 - 1472*K2**2 + 280*K2*K3*K5 + 64*K2*K4*K6 - 704*K3**2 - 336*K4**2 - 88*K5**2 - 16*K6**2 + 1470 |
| 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}], [{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}], [{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}], [{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}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{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}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {3, 4}, {2}, {1}]] |
| If K is slice | False |