| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,0,1,2,0,1,1,1,1,0,1,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1802'] |
| 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+20t^5+33t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1802'] |
| 2-strand cable arrow polynomial of the knot is: -3088*K1**4 + 480*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1984*K1**3*K3 + 224*K1**2*K2**2*K4 - 1648*K1**2*K2**2 + 96*K1**2*K2*K4**2 - 1664*K1**2*K2*K4 + 7280*K1**2*K2 - 944*K1**2*K3**2 - 688*K1**2*K4**2 - 96*K1**2*K4*K6 - 4668*K1**2 - 128*K1*K2**2*K3 - 320*K1*K2**2*K5 - 480*K1*K2*K3*K4 + 6120*K1*K2*K3 + 2664*K1*K3*K4 + 832*K1*K4*K5 + 24*K1*K5*K6 - 72*K2**4 - 112*K2**2*K4**2 + 1144*K2**2*K4 - 3660*K2**2 + 304*K2*K3*K5 + 112*K2*K4*K6 - 2160*K3**2 - 1214*K4**2 - 220*K5**2 - 28*K6**2 + 3828 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1802'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13907', 'vk6.14004', 'vk6.14191', 'vk6.14430', 'vk6.14982', 'vk6.15105', 'vk6.15659', 'vk6.16113', 'vk6.16709', 'vk6.16734', 'vk6.16849', 'vk6.18805', 'vk6.19276', 'vk6.19568', 'vk6.23143', 'vk6.23228', 'vk6.25399', 'vk6.26463', 'vk6.33718', 'vk6.33795', 'vk6.34278', 'vk6.35141', 'vk6.37532', 'vk6.42731', 'vk6.44691', 'vk6.54126', 'vk6.54914', 'vk6.54937', 'vk6.56407', 'vk6.56599', 'vk6.59338', 'vk6.64605'] |
| 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 | O1O2O3U4U3O5O6U1U6O4U5U2 |
| R3 orbit | {'O1O2O3U4U3O5O6U1U6O4U5U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U4O5U6U3O6O4U1U5 |
| Gauss code of K* | O1O2U3O4O5U1U5U6O3O6U4U2 |
| Gauss code of -K* | O1O2U3O4O5U4U2O6O3U6U1U5 |
| 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 -1 0 1],[ 2 0 2 0 0 1 1],[-1 -2 0 1 -1 -1 0],[-1 0 -1 0 -1 -1 0],[ 1 0 1 1 0 0 1],[ 0 -1 1 1 0 0 0],[-1 -1 0 0 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 -1 -1 -2],[-1 -1 0 0 -1 -1 0],[-1 0 0 0 0 -1 -1],[ 0 1 1 0 0 0 -1],[ 1 1 1 1 0 0 0],[ 2 2 0 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,1,1,2,0,1,1,0,0,1,1,0,1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,0,1,2,0,1,1,1,1,0,1,0,-1,0] |
| Phi of -K | [-2,-1,0,1,1,1,1,1,1,2,3,1,1,1,1,0,1,0,0,-1,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,0,1,3,0,0,1,1,1,1,2,1,1,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,1,0,1,2,0,1,1,1,1,0,1,0,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 5z^2+24z+29 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+24w^2z+29w |
| Inner characteristic polynomial | t^6+12t^4+16t^2+1 |
| Outer characteristic polynomial | t^7+20t^5+33t^3+6t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -3088*K1**4 + 480*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1984*K1**3*K3 + 224*K1**2*K2**2*K4 - 1648*K1**2*K2**2 + 96*K1**2*K2*K4**2 - 1664*K1**2*K2*K4 + 7280*K1**2*K2 - 944*K1**2*K3**2 - 688*K1**2*K4**2 - 96*K1**2*K4*K6 - 4668*K1**2 - 128*K1*K2**2*K3 - 320*K1*K2**2*K5 - 480*K1*K2*K3*K4 + 6120*K1*K2*K3 + 2664*K1*K3*K4 + 832*K1*K4*K5 + 24*K1*K5*K6 - 72*K2**4 - 112*K2**2*K4**2 + 1144*K2**2*K4 - 3660*K2**2 + 304*K2*K3*K5 + 112*K2*K4*K6 - 2160*K3**2 - 1214*K4**2 - 220*K5**2 - 28*K6**2 + 3828 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {3, 5}, {2, 4}], [{2, 6}, {1, 5}, {3, 4}], [{3, 6}, {1, 5}, {2, 4}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {3, 4}, {1, 2}], [{6}, {3, 5}, {2, 4}, {1}]] |
| If K is slice | False |