| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,1,2,3,1,1,1,1,0,1,0,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1167'] |
| Arrow polynomial of the knot is: -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.217', '6.219', '6.304', '6.349', '6.390', '6.400', '6.416', '6.515', '6.518', '6.530', '6.582', '6.616', '6.629', '6.641', '6.645', '6.702', '6.710', '6.715', '6.729', '6.733', '6.734', '6.802', '6.840', '6.845', '6.854', '6.860', '6.900', '6.905', '6.921', '6.924', '6.979', '6.980', '6.996', '6.1044', '6.1067', '6.1086', '6.1100', '6.1139', '6.1145', '6.1149', '6.1167', '6.1169', '6.1183', '6.1314'] |
| Outer characteristic polynomial of the knot is: t^7+54t^5+81t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1167'] |
| 2-strand cable arrow polynomial of the knot is: -1440*K1**2*K2**2 - 32*K1**2*K2*K4 + 2536*K1**2*K2 - 2496*K1**2 + 320*K1*K2**3*K3 + 96*K1*K2**2*K3*K4 - 768*K1*K2**2*K3 - 384*K1*K2**2*K5 - 384*K1*K2*K3*K4 + 3144*K1*K2*K3 + 432*K1*K3*K4 + 200*K1*K4*K5 - 984*K2**4 - 704*K2**2*K3**2 - 72*K2**2*K4**2 + 1552*K2**2*K4 - 2174*K2**2 + 944*K2*K3*K5 + 16*K2*K4*K6 - 1208*K3**2 - 490*K4**2 - 256*K5**2 - 2*K6**2 + 2152 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1167'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16370', 'vk6.16411', 'vk6.18113', 'vk6.18449', 'vk6.22704', 'vk6.22805', 'vk6.24566', 'vk6.24983', 'vk6.34677', 'vk6.34756', 'vk6.36703', 'vk6.37125', 'vk6.42330', 'vk6.42374', 'vk6.43979', 'vk6.44293', 'vk6.54629', 'vk6.54654', 'vk6.55925', 'vk6.56217', 'vk6.59108', 'vk6.59175', 'vk6.60455', 'vk6.60816', 'vk6.64655', 'vk6.64703', 'vk6.65573', 'vk6.65883', 'vk6.68005', 'vk6.68031', 'vk6.68653', 'vk6.68866'] |
| 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 | O1O2O3O4U1U5U2O5O6U4U3U6 |
| R3 orbit | {'O1O2O3O4U1U5U2O5O6U4U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U2U1O5O6U3U6U4 |
| Gauss code of K* | O1O2O3U2U4O5O6O4U1U3U6U5 |
| Gauss code of -K* | O1O2O3U1U4O5O4O6U3U2U5U6 |
| 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 -3 0 1 1 -1 2],[ 3 0 1 3 2 2 2],[ 0 -1 0 1 0 0 2],[-1 -3 -1 0 0 -1 2],[-1 -2 0 0 0 -1 1],[ 1 -2 0 1 1 0 2],[-2 -2 -2 -2 -1 -2 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 -1 -2 -2 -2 -2],[-1 1 0 0 0 -1 -2],[-1 2 0 0 -1 -1 -3],[ 0 2 0 1 0 0 -1],[ 1 2 1 1 0 0 -2],[ 3 2 2 3 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,1,2,2,2,2,0,0,1,2,1,1,3,0,1,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,1,2,3,1,1,1,1,0,1,0,0,-1,0] |
| Phi of -K | [-3,-1,0,1,1,2,0,2,1,2,3,1,1,1,1,0,1,0,0,-1,0] |
| Phi of K* | [-2,-1,-1,0,1,3,-1,0,0,1,3,0,0,1,1,1,1,2,1,2,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,1,2,3,2,0,1,1,2,0,1,2,0,1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 6z^2+19z+15 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+8w^3z^2-6w^3z+25w^2z+15w |
| Inner characteristic polynomial | t^6+38t^4+32t^2+1 |
| Outer characteristic polynomial | t^7+54t^5+81t^3+8t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -1440*K1**2*K2**2 - 32*K1**2*K2*K4 + 2536*K1**2*K2 - 2496*K1**2 + 320*K1*K2**3*K3 + 96*K1*K2**2*K3*K4 - 768*K1*K2**2*K3 - 384*K1*K2**2*K5 - 384*K1*K2*K3*K4 + 3144*K1*K2*K3 + 432*K1*K3*K4 + 200*K1*K4*K5 - 984*K2**4 - 704*K2**2*K3**2 - 72*K2**2*K4**2 + 1552*K2**2*K4 - 2174*K2**2 + 944*K2*K3*K5 + 16*K2*K4*K6 - 1208*K3**2 - 490*K4**2 - 256*K5**2 - 2*K6**2 + 2152 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |