Gauss code |
O1O2O3O4U2U1U4O5O6U5U3U6 |
R3 orbit |
{'O1O2O3O4U2U1U4O5O6U5U3U6'} |
R3 orbit length |
1 |
Gauss code of -K |
O1O2O3O4U5U2U6O5O6U1U4U3 |
Gauss code of K* |
O1O2O3U4U5O4O6O5U2U1U6U3 |
Gauss code of -K* |
O1O2O3U1U3O4O5O6U4U2U6U5 |
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 2 -1 2],[ 2 0 0 3 2 0 1],[ 2 0 0 2 1 0 1],[-1 -3 -2 0 0 0 2],[-2 -2 -1 0 0 0 0],[ 1 0 0 0 0 0 1],[-2 -1 -1 -2 0 -1 0]] |
Primitive based matrix |
[[ 0 2 2 1 -1 -2 -2],[-2 0 0 0 0 -1 -2],[-2 0 0 -2 -1 -1 -1],[-1 0 2 0 0 -2 -3],[ 1 0 1 0 0 0 0],[ 2 1 1 2 0 0 0],[ 2 2 1 3 0 0 0]] |
If based matrix primitive |
True |
Phi of primitive based matrix |
[-2,-2,-1,1,2,2,0,0,0,1,2,2,1,1,1,0,2,3,0,0,0] |
Phi over symmetry |
[-2,-2,-1,1,2,2,0,-1,2,3,3,1,3,2,3,2,0,1,1,1,0] |
Phi of -K |
[-2,-2,-1,1,2,2,0,1,0,2,3,1,1,3,3,2,3,2,1,-1,0] |
Phi of K* |
[-2,-2,-1,1,2,2,0,-1,2,3,3,1,3,2,3,2,0,1,1,1,0] |
Phi of -K* |
[-2,-2,-1,1,2,2,0,0,2,1,1,0,3,1,2,0,1,0,2,0,0] |
Symmetry type of based matrix |
c |
u-polynomial |
0 |
Normalized Jones-Krushkal polynomial |
8z^2+27z+23 |
Enhanced Jones-Krushkal polynomial |
8w^3z^2+27w^2z+23w |
Inner characteristic polynomial |
t^6+25t^4+41t^2+1 |
Outer characteristic polynomial |
t^7+43t^5+129t^3+6t |
Flat arrow polynomial |
4*K1**2*K2 - 2*K1**2 - 2*K1*K3 - 2*K2**2 + K4 + 2 |
2-strand cable arrow polynomial |
-64*K1**3*K3 + 224*K1**2*K2**2*K4 - 1952*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 928*K1**2*K2*K4 + 3984*K1**2*K2 - 128*K1**2*K3**2 - 288*K1**2*K4**2 - 4104*K1**2 + 288*K1*K2**3*K3 + 192*K1*K2**2*K3*K4 - 1376*K1*K2**2*K3 - 192*K1*K2**2*K5 - 576*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 4832*K1*K2*K3 - 224*K1*K2*K4*K5 - 96*K1*K2*K4*K7 + 1920*K1*K3*K4 + 496*K1*K4*K5 + 32*K1*K5*K6 + 24*K1*K6*K7 - 32*K2**4*K4**2 + 128*K2**4*K4 - 760*K2**4 + 32*K2**3*K4*K6 - 32*K2**3*K6 - 768*K2**2*K3**2 - 32*K2**2*K3*K7 + 32*K2**2*K4**3 - 384*K2**2*K4**2 - 32*K2**2*K4*K8 + 2264*K2**2*K4 - 8*K2**2*K6**2 - 3636*K2**2 - 64*K2*K3**2*K4 - 64*K2*K3*K4*K5 + 856*K2*K3*K5 + 392*K2*K4*K6 + 112*K2*K5*K7 + 8*K2*K6*K8 + 48*K3**2*K6 - 1944*K3**2 + 88*K3*K4*K7 - 8*K4**4 + 8*K4**2*K8 - 1320*K4**2 - 264*K5**2 - 68*K6**2 - 64*K7**2 - 2*K8**2 + 3416 |
Genus of based matrix |
1 |
Fillings of based matrix |
[[{1, 6}, {3, 5}, {2, 4}], [{2, 6}, {3, 5}, {1, 4}]] |
If K is slice |
False |