| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,2,1,1,2,1,0,0,1,1,2,-1,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1508'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1**2 - 8*K1*K2 + K1 + K2 + 3*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.1030', '6.1062', '6.1226', '6.1508', '6.1525', '6.1596', '6.1724', '6.1729', '6.1735', '6.1738', '6.1789', '6.1809', '6.1921'] |
| Outer characteristic polynomial of the knot is: t^7+28t^5+60t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1508'] |
| 2-strand cable arrow polynomial of the knot is: 800*K1**4*K2 - 2432*K1**4 + 128*K1**3*K2*K3 - 96*K1**3*K3 + 736*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 6256*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 512*K1**2*K2*K4 + 8584*K1**2*K2 - 416*K1**2*K3**2 - 32*K1**2*K4**2 - 5092*K1**2 + 512*K1*K2**3*K3 - 2496*K1*K2**2*K3 - 480*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 7944*K1*K2*K3 + 1424*K1*K3*K4 + 112*K1*K4*K5 - 32*K2**6 + 224*K2**4*K4 - 1464*K2**4 - 96*K2**3*K6 - 704*K2**2*K3**2 - 128*K2**2*K4**2 + 2552*K2**2*K4 - 4850*K2**2 + 736*K2*K3*K5 + 72*K2*K4*K6 - 2324*K3**2 - 866*K4**2 - 168*K5**2 - 6*K6**2 + 4592 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1508'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11488', 'vk6.11794', 'vk6.12812', 'vk6.13145', 'vk6.17062', 'vk6.17304', 'vk6.20903', 'vk6.21065', 'vk6.22315', 'vk6.22493', 'vk6.23787', 'vk6.28381', 'vk6.31249', 'vk6.31600', 'vk6.32822', 'vk6.35578', 'vk6.36032', 'vk6.40031', 'vk6.40314', 'vk6.42085', 'vk6.43277', 'vk6.46563', 'vk6.46771', 'vk6.48028', 'vk6.52251', 'vk6.53408', 'vk6.57709', 'vk6.57719', 'vk6.58895', 'vk6.59949', 'vk6.64422', 'vk6.69757'] |
| 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 | O1O2O3U2O4U1U3O5O6U4U6U5 |
| R3 orbit | {'O1O2O3U2O4U1U3O5O6U4U6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U6O5O4U1U3O6U2 |
| Gauss code of K* | O1O2O3U4U5U6O5U1O4O6U3U2 |
| Gauss code of -K* | O1O2O3U2U1O4O5U3O6U4U6U5 |
| 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 -1 1 0 1 1],[ 2 0 0 2 2 1 1],[ 1 0 0 1 1 0 0],[-1 -2 -1 0 1 1 1],[ 0 -2 -1 -1 0 2 1],[-1 -1 0 -1 -2 0 0],[-1 -1 0 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 1 1 -1 -2],[-1 -1 0 0 -1 0 -1],[-1 -1 0 0 -2 0 -1],[ 0 -1 1 2 0 -1 -2],[ 1 1 0 0 1 0 0],[ 2 2 1 1 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,-1,-1,1,2,0,1,0,1,2,0,1,1,2,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,2,1,1,2,1,0,0,1,1,2,-1,0,-1,-1] |
| Phi of -K | [-2,-1,0,1,1,1,1,0,1,2,2,0,1,2,2,2,-1,0,-1,-1,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,-1,2,2,1,2,1,1,0,2,2,0,0,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,2,1,1,2,1,0,0,1,1,2,-1,0,-1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 7z^2+28z+29 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2+28w^2z+29w |
| Inner characteristic polynomial | t^6+20t^4+17t^2+1 |
| Outer characteristic polynomial | t^7+28t^5+60t^3+11t |
| Flat arrow polynomial | 4*K1**3 - 2*K1**2 - 8*K1*K2 + K1 + K2 + 3*K3 + 2 |
| 2-strand cable arrow polynomial | 800*K1**4*K2 - 2432*K1**4 + 128*K1**3*K2*K3 - 96*K1**3*K3 + 736*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 6256*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 512*K1**2*K2*K4 + 8584*K1**2*K2 - 416*K1**2*K3**2 - 32*K1**2*K4**2 - 5092*K1**2 + 512*K1*K2**3*K3 - 2496*K1*K2**2*K3 - 480*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 7944*K1*K2*K3 + 1424*K1*K3*K4 + 112*K1*K4*K5 - 32*K2**6 + 224*K2**4*K4 - 1464*K2**4 - 96*K2**3*K6 - 704*K2**2*K3**2 - 128*K2**2*K4**2 + 2552*K2**2*K4 - 4850*K2**2 + 736*K2*K3*K5 + 72*K2*K4*K6 - 2324*K3**2 - 866*K4**2 - 168*K5**2 - 6*K6**2 + 4592 |
| 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}], [{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}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {1, 4}, {3}, {2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {2, 3}, {1}]] |
| If K is slice | False |