| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,0,1,1,2,0,1,2,2,1,1,1,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1249'] |
| Arrow polynomial of the knot is: -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.120', '6.213', '6.216', '6.320', '6.322', '6.615', '6.617', '6.891', '6.951', '6.955', '6.1001', '6.1012', '6.1022', '6.1043', '6.1047', '6.1063', '6.1074', '6.1249', '6.1544', '6.1546', '6.1555', '6.1573', '6.1574', '6.1585', '6.1756', '6.1757', '6.1762', '6.1802', '6.1803', '6.1824', '6.1881', '6.1935'] |
| Outer characteristic polynomial of the knot is: t^7+26t^5+58t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1249'] |
| 2-strand cable arrow polynomial of the knot is: -1072*K1**4 + 160*K1**3*K2*K3 - 96*K1**3*K3 - 1472*K1**2*K2**2 - 32*K1**2*K2*K4 + 2840*K1**2*K2 - 1904*K1**2*K3**2 - 3644*K1**2 - 416*K1*K2**2*K3 + 32*K1*K2*K3**3 + 5816*K1*K2*K3 - 32*K1*K3**2*K5 + 2848*K1*K3*K4 + 8*K1*K5*K6 - 72*K2**4 - 304*K2**2*K3**2 - 80*K2**2*K4**2 + 576*K2**2*K4 - 3180*K2**2 - 64*K2*K3**2*K4 + 400*K2*K3*K5 + 152*K2*K4*K6 - 64*K3**4 + 120*K3**2*K6 - 3000*K3**2 - 1150*K4**2 - 124*K5**2 - 84*K6**2 + 3836 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1249'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3628', 'vk6.3713', 'vk6.3904', 'vk6.4011', 'vk6.7054', 'vk6.7109', 'vk6.7284', 'vk6.7385', 'vk6.11404', 'vk6.12587', 'vk6.12698', 'vk6.19113', 'vk6.19158', 'vk6.19805', 'vk6.25726', 'vk6.25785', 'vk6.26238', 'vk6.26683', 'vk6.31012', 'vk6.31139', 'vk6.32192', 'vk6.37841', 'vk6.37896', 'vk6.44959', 'vk6.48256', 'vk6.48435', 'vk6.50016', 'vk6.50159', 'vk6.52152', 'vk6.63735', 'vk6.66206', 'vk6.66233'] |
| 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 | O1O2O3O4U3U5U4O6O5U2U1U6 |
| R3 orbit | {'O1O2O3O4U3U5U4O6O5U2U1U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U4U3O6O5U1U6U2 |
| Gauss code of K* | O1O2O3U4U2O5O6O4U6U5U1U3 |
| Gauss code of -K* | O1O2O3U4U1O5O4O6U5U6U3U2 |
| 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 -1 -1 -1 2 0 1],[ 1 0 0 -1 2 0 1],[ 1 0 0 -1 2 0 0],[ 1 1 1 0 1 0 0],[-2 -2 -2 -1 0 -2 -1],[ 0 0 0 0 2 0 1],[-1 -1 0 0 1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 -1 -2 -1 -2 -2],[-1 1 0 -1 0 0 -1],[ 0 2 1 0 0 0 0],[ 1 1 0 0 0 1 1],[ 1 2 0 0 -1 0 0],[ 1 2 1 0 -1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,1,2,1,2,2,1,0,0,1,0,0,0,-1,-1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,0,1,1,2,0,1,2,2,1,1,1,0,-1,-1] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,-1,1,2,2,0,1,1,1,1,2,1,0,0,0] |
| Phi of K* | [-2,-1,0,1,1,1,0,0,1,1,2,0,1,2,2,1,1,1,0,-1,-1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,0,2,1,0,0,1,0,1,2,1,2,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 6z^2+27z+31 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2+27w^2z+31w |
| Inner characteristic polynomial | t^6+18t^4+25t^2+4 |
| Outer characteristic polynomial | t^7+26t^5+58t^3+11t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -1072*K1**4 + 160*K1**3*K2*K3 - 96*K1**3*K3 - 1472*K1**2*K2**2 - 32*K1**2*K2*K4 + 2840*K1**2*K2 - 1904*K1**2*K3**2 - 3644*K1**2 - 416*K1*K2**2*K3 + 32*K1*K2*K3**3 + 5816*K1*K2*K3 - 32*K1*K3**2*K5 + 2848*K1*K3*K4 + 8*K1*K5*K6 - 72*K2**4 - 304*K2**2*K3**2 - 80*K2**2*K4**2 + 576*K2**2*K4 - 3180*K2**2 - 64*K2*K3**2*K4 + 400*K2*K3*K5 + 152*K2*K4*K6 - 64*K3**4 + 120*K3**2*K6 - 3000*K3**2 - 1150*K4**2 - 124*K5**2 - 84*K6**2 + 3836 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}]] |
| If K is slice | False |