Gauss code |
O1O2O3O4U5U3O6O5U1U6U4U2 |
R3 orbit |
{'O1O2O3O4U5U3O6O5U1U6U4U2'} |
R3 orbit length |
1 |
Gauss code of -K |
O1O2O3O4U3U1U5U4O6O5U2U6 |
Gauss code of K* |
O1O2O3O4U1U4U5U3O6O5U2U6 |
Gauss code of -K* |
O1O2O3O4U5U3O6O5U2U6U1U4 |
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 1 0 2 0 0],[ 3 0 3 1 3 2 0],[-1 -3 0 0 1 -1 -1],[ 0 -1 0 0 0 0 -1],[-2 -3 -1 0 0 -1 -1],[ 0 -2 1 0 1 0 0],[ 0 0 1 1 1 0 0]] |
Primitive based matrix |
[[ 0 2 1 0 0 0 -3],[-2 0 -1 0 -1 -1 -3],[-1 1 0 0 -1 -1 -3],[ 0 0 0 0 0 -1 -1],[ 0 1 1 0 0 0 -2],[ 0 1 1 1 0 0 0],[ 3 3 3 1 2 0 0]] |
If based matrix primitive |
True |
Phi of primitive based matrix |
[-2,-1,0,0,0,3,1,0,1,1,3,0,1,1,3,0,1,1,0,2,0] |
Phi over symmetry |
[-3,0,0,0,1,2,0,1,2,3,3,1,0,1,1,0,0,0,1,1,1] |
Phi of -K |
[-3,0,0,0,1,2,1,2,3,1,2,0,0,0,1,1,1,2,0,1,0] |
Phi of K* |
[-2,-1,0,0,0,3,0,1,1,2,2,0,0,1,1,0,0,1,1,3,2] |
Phi of -K* |
[-3,0,0,0,1,2,0,1,2,3,3,1,0,1,1,0,0,0,1,1,1] |
Symmetry type of based matrix |
c |
u-polynomial |
t^3-t^2-t |
Normalized Jones-Krushkal polynomial |
4z^2+23z+31 |
Enhanced Jones-Krushkal polynomial |
4w^3z^2-2w^3z+25w^2z+31w |
Inner characteristic polynomial |
t^6+29t^4+30t^2+4 |
Outer characteristic polynomial |
t^7+43t^5+71t^3+13t |
Flat arrow polynomial |
20*K1**3 - 10*K1**2 - 10*K1*K2 - 10*K1 + 5*K2 + 6 |
2-strand cable arrow polynomial |
-192*K1**4*K2**2 + 768*K1**4*K2 - 1792*K1**4 + 224*K1**3*K2*K3 - 256*K1**3*K3 - 256*K1**2*K2**4 + 1696*K1**2*K2**3 - 8560*K1**2*K2**2 - 544*K1**2*K2*K4 + 9992*K1**2*K2 - 96*K1**2*K3**2 - 6724*K1**2 + 1376*K1*K2**3*K3 - 1888*K1*K2**2*K3 - 384*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 8880*K1*K2*K3 + 744*K1*K3*K4 + 96*K1*K4*K5 - 416*K2**6 + 544*K2**4*K4 - 3768*K2**4 - 64*K2**3*K6 - 1184*K2**2*K3**2 - 264*K2**2*K4**2 + 3704*K2**2*K4 - 4416*K2**2 + 680*K2*K3*K5 + 128*K2*K4*K6 - 2332*K3**2 - 938*K4**2 - 120*K5**2 - 24*K6**2 + 5512 |
Genus of based matrix |
1 |
Fillings of based matrix |
[[{1, 6}, {2, 5}, {3, 4}]] |
If K is slice |
False |