| Min(phi) over symmetries of the knot is: [-3,-1,-1,1,2,2,0,1,3,2,3,0,1,1,1,2,2,2,2,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.377'] |
| Arrow polynomial of the knot is: -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.377', '6.638', '6.646', '6.647', '6.657', '6.658', '6.662', '6.692', '6.695', '6.714', '6.720', '6.726', '6.730', '6.731', '6.749', '6.756', '6.772', '6.779', '6.781', '6.800', '6.829', '6.1085', '6.1089', '6.1302', '6.1349', '6.1350', '6.1360', '6.1362', '6.1375', '6.1384'] |
| Outer characteristic polynomial of the knot is: t^7+64t^5+32t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.377'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 160*K1**4*K2 - 880*K1**4 + 96*K1**3*K2*K3 - 1200*K1**2*K2**2 + 1648*K1**2*K2 - 176*K1**2*K3**2 - 536*K1**2 + 1112*K1*K2*K3 + 160*K1*K3*K4 + 8*K1*K4*K5 - 384*K2**4 - 144*K2**2*K3**2 - 8*K2**2*K4**2 + 232*K2**2*K4 - 438*K2**2 + 104*K2*K3*K5 + 8*K2*K4*K6 - 268*K3**2 - 68*K4**2 - 20*K5**2 - 2*K6**2 + 658 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.377'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16533', 'vk6.16624', 'vk6.17521', 'vk6.17577', 'vk6.18874', 'vk6.18950', 'vk6.19215', 'vk6.19510', 'vk6.20056', 'vk6.21186', 'vk6.23056', 'vk6.23469', 'vk6.24119', 'vk6.25500', 'vk6.25573', 'vk6.26023', 'vk6.26409', 'vk6.27121', 'vk6.28656', 'vk6.35049', 'vk6.35602', 'vk6.36302', 'vk6.36370', 'vk6.37601', 'vk6.37688', 'vk6.38321', 'vk6.38514', 'vk6.38903', 'vk6.40462', 'vk6.41104', 'vk6.42507', 'vk6.43479', 'vk6.44604', 'vk6.45197', 'vk6.45414', 'vk6.45656', 'vk6.54761', 'vk6.56439', 'vk6.56862', 'vk6.57838', 'vk6.60179', 'vk6.61164', 'vk6.61391', 'vk6.62406', 'vk6.62804', 'vk6.65019', 'vk6.66569', 'vk6.69221'] |
| 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 | O1O2O3O4O5U4U1O6U3U5U6U2 |
| R3 orbit | {'O1O2O3O4O5U4U1O6U3U5U6U2', 'O1O2O3O4O5U4U1U2O6U5U3U6', 'O1O2O3O4U3O5U1U2O6U4U5U6'} |
| R3 orbit length | 3 |
| Gauss code of -K | O1O2O3O4O5U4U6U1U3O6U5U2 |
| Gauss code of K* | O1O2O3O4U5U4U1U6U2O6O5U3 |
| Gauss code of -K* | O1O2O3O4U2O5O6U3U6U4U1U5 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 1 -1 -1 2 2],[ 3 0 3 1 0 3 2],[-1 -3 0 -2 -1 1 2],[ 1 -1 2 0 0 2 2],[ 1 0 1 0 0 1 1],[-2 -3 -1 -2 -1 0 1],[-2 -2 -2 -2 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 -1 -1 -3],[-2 0 1 -1 -1 -2 -3],[-2 -1 0 -2 -1 -2 -2],[-1 1 2 0 -1 -2 -3],[ 1 1 1 1 0 0 0],[ 1 2 2 2 0 0 -1],[ 3 3 2 3 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,1,1,3,-1,1,1,2,3,2,1,2,2,1,2,3,0,0,1] |
| Phi over symmetry | [-3,-1,-1,1,2,2,0,1,3,2,3,0,1,1,1,2,2,2,2,1,-1] |
| Phi of -K | [-3,-1,-1,1,2,2,1,2,1,2,3,0,0,1,1,1,2,2,0,-1,-1] |
| Phi of K* | [-2,-2,-1,1,1,3,-1,-1,1,2,3,0,1,2,2,0,1,1,0,1,2] |
| Phi of -K* | [-3,-1,-1,1,2,2,0,1,3,2,3,0,1,1,1,2,2,2,2,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-2t^2+t |
| Normalized Jones-Krushkal polynomial | 8z+17 |
| Enhanced Jones-Krushkal polynomial | 8w^2z+17w |
| Inner characteristic polynomial | t^6+44t^4+8t^2 |
| Outer characteristic polynomial | t^7+64t^5+32t^3 |
| Flat arrow polynomial | -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 160*K1**4*K2 - 880*K1**4 + 96*K1**3*K2*K3 - 1200*K1**2*K2**2 + 1648*K1**2*K2 - 176*K1**2*K3**2 - 536*K1**2 + 1112*K1*K2*K3 + 160*K1*K3*K4 + 8*K1*K4*K5 - 384*K2**4 - 144*K2**2*K3**2 - 8*K2**2*K4**2 + 232*K2**2*K4 - 438*K2**2 + 104*K2*K3*K5 + 8*K2*K4*K6 - 268*K3**2 - 68*K4**2 - 20*K5**2 - 2*K6**2 + 658 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{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}], [{3, 6}, {5}, {4}, {2}, {1}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |