Gauss code |
O1O2O3O4O5U4U2O6U3U1U6U5 |
R3 orbit |
{'O1O2O3O4O5U4U2O6U3U1U6U5'} |
R3 orbit length |
1 |
Gauss code of -K |
O1O2O3O4O5U1U6U5U3O6U4U2 |
Gauss code of K* |
O1O2O3O4U2U5U1U6U4O6O5U3 |
Gauss code of -K* |
O1O2O3O4U2O5O6U1U6U4U5U3 |
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 -2 -1 -1 4 2],[ 2 0 -1 1 0 5 2],[ 2 1 0 1 0 3 1],[ 1 -1 -1 0 0 3 1],[ 1 0 0 0 0 1 0],[-4 -5 -3 -3 -1 0 0],[-2 -2 -1 -1 0 0 0]] |
Primitive based matrix |
[[ 0 4 2 -1 -1 -2 -2],[-4 0 0 -1 -3 -3 -5],[-2 0 0 0 -1 -1 -2],[ 1 1 0 0 0 0 0],[ 1 3 1 0 0 -1 -1],[ 2 3 1 0 1 0 1],[ 2 5 2 0 1 -1 0]] |
If based matrix primitive |
True |
Phi of primitive based matrix |
[-4,-2,1,1,2,2,0,1,3,3,5,0,1,1,2,0,0,0,1,1,-1] |
Phi over symmetry |
[-4,-2,1,1,2,2,0,1,3,3,5,0,1,1,2,0,0,0,1,1,-1] |
Phi of -K |
[-2,-2,-1,-1,2,4,-1,0,1,3,3,0,1,2,1,0,2,2,3,4,2] |
Phi of K* |
[-4,-2,1,1,2,2,2,2,4,1,3,2,3,2,3,0,0,0,1,1,-1] |
Phi of -K* |
[-2,-2,-1,-1,2,4,-1,0,1,2,5,0,1,1,3,0,0,1,1,3,0] |
Symmetry type of based matrix |
c |
u-polynomial |
-t^4+t^2+2t |
Normalized Jones-Krushkal polynomial |
2z^2+19z+31 |
Enhanced Jones-Krushkal polynomial |
2w^3z^2+19w^2z+31w |
Inner characteristic polynomial |
t^6+53t^4+12t^2 |
Outer characteristic polynomial |
t^7+83t^5+67t^3+4t |
Flat arrow polynomial |
8*K1**3 - 8*K1**2 - 8*K1*K2 - 2*K1*K3 - 2*K1 + 5*K2 + 2*K3 + K4 + 5 |
2-strand cable arrow polynomial |
-128*K1**4*K2**2 + 544*K1**4*K2 - 1040*K1**4 + 96*K1**3*K2*K3 - 384*K1**3*K3 + 576*K1**2*K2**3 - 3872*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 128*K1**2*K2*K4 + 6280*K1**2*K2 - 384*K1**2*K3**2 - 32*K1**2*K3*K5 - 5320*K1**2 + 608*K1*K2**3*K3 - 1408*K1*K2**2*K3 - 224*K1*K2**2*K5 + 64*K1*K2*K3**3 - 288*K1*K2*K3*K4 + 6216*K1*K2*K3 + 1088*K1*K3*K4 + 232*K1*K4*K5 + 24*K1*K5*K6 - 64*K2**6 + 192*K2**4*K4 - 1200*K2**4 + 32*K2**3*K3*K5 - 64*K2**3*K6 - 800*K2**2*K3**2 - 128*K2**2*K4**2 + 1680*K2**2*K4 - 32*K2**2*K5**2 - 8*K2**2*K6**2 - 4060*K2**2 - 32*K2*K3**2*K4 - 32*K2*K3*K4*K5 + 856*K2*K3*K5 + 104*K2*K4*K6 + 40*K2*K5*K7 + 8*K2*K6*K8 - 48*K3**4 + 72*K3**2*K6 - 2320*K3**2 + 16*K3*K4*K7 - 758*K4**2 - 320*K5**2 - 60*K6**2 - 16*K7**2 - 2*K8**2 + 4358 |
Genus of based matrix |
1 |
Fillings of based matrix |
[[{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {1, 4}, {2, 3}]] |
If K is slice |
False |