Gauss code |
O1O2O3O4O5U4U1U3O6U5U2U6 |
R3 orbit |
{'O1O2O3O4O5U4U1U3O6U5U2U6'} |
R3 orbit length |
1 |
Gauss code of -K |
O1O2O3O4O5U6U4U1O6U3U5U2 |
Gauss code of K* |
O1O2O3U4O5O6O4U2U6U3U1U5 |
Gauss code of -K* |
O1O2O3U1O4O5O6U3U6U4U2U5 |
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 0 -1 2 2],[ 3 0 3 1 0 3 2],[ 0 -3 0 -1 -1 2 2],[ 0 -1 1 0 0 2 1],[ 1 0 1 0 0 1 1],[-2 -3 -2 -2 -1 0 1],[-2 -2 -2 -1 -1 -1 0]] |
Primitive based matrix |
[[ 0 2 2 0 0 -1 -3],[-2 0 1 -2 -2 -1 -3],[-2 -1 0 -1 -2 -1 -2],[ 0 2 1 0 1 0 -1],[ 0 2 2 -1 0 -1 -3],[ 1 1 1 0 1 0 0],[ 3 3 2 1 3 0 0]] |
If based matrix primitive |
True |
Phi of primitive based matrix |
[-2,-2,0,0,1,3,-1,2,2,1,3,1,2,1,2,-1,0,1,1,3,0] |
Phi over symmetry |
[-3,-1,0,0,2,2,0,1,3,2,3,0,1,1,1,1,1,2,2,2,-1] |
Phi of -K |
[-3,-1,0,0,2,2,2,0,2,2,3,0,1,2,2,1,0,0,0,1,-1] |
Phi of K* |
[-2,-2,0,0,1,3,-1,0,1,2,3,0,0,2,2,-1,0,0,1,2,2] |
Phi of -K* |
[-3,-1,0,0,2,2,0,1,3,2,3,0,1,1,1,1,1,2,2,2,-1] |
Symmetry type of based matrix |
c |
u-polynomial |
t^3-2t^2+t |
Normalized Jones-Krushkal polynomial |
z^2+18z+33 |
Enhanced Jones-Krushkal polynomial |
w^3z^2+18w^2z+33w |
Inner characteristic polynomial |
t^6+41t^4+16t^2 |
Outer characteristic polynomial |
t^7+59t^5+64t^3+4t |
Flat arrow polynomial |
4*K1**3 - 8*K1**2 - 6*K1*K2 + 4*K2 + 2*K3 + 5 |
2-strand cable arrow polynomial |
-128*K1**4*K2**2 + 256*K1**4*K2 - 1312*K1**4 + 544*K1**3*K2*K3 - 288*K1**3*K3 + 320*K1**2*K2**3 - 3344*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 256*K1**2*K2*K4 + 5808*K1**2*K2 - 768*K1**2*K3**2 - 4504*K1**2 + 192*K1*K2**3*K3 - 832*K1*K2**2*K3 - 96*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 5280*K1*K2*K3 + 1248*K1*K3*K4 + 48*K1*K4*K5 - 32*K2**6 + 96*K2**4*K4 - 544*K2**4 - 32*K2**3*K6 - 432*K2**2*K3**2 - 88*K2**2*K4**2 + 944*K2**2*K4 - 3556*K2**2 - 32*K2*K3**2*K4 + 632*K2*K3*K5 + 88*K2*K4*K6 + 40*K3**2*K6 - 2028*K3**2 - 584*K4**2 - 188*K5**2 - 36*K6**2 + 3742 |
Genus of based matrix |
1 |
Fillings of based matrix |
[[{1, 6}, {3, 5}, {2, 4}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{4, 6}, {2, 5}, {1, 3}]] |
If K is slice |
False |