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Flat knot 6.485

Min(phi) over symmetries of the knot is: [-4,-1,0,1,2,2,1,4,3,2,2,2,2,1,1,1,1,2,0,1,0]
Flat knots (up to 7 crossings) with same phi are :['6.485']
Arrow polynomial of the knot is: -2*K1**2 - 2*K1*K3 + 2*K2 + K4 + 2
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.175', '6.485']
Outer characteristic polynomial of the knot is: t^7+77t^5+125t^3
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.485']
2-strand cable arrow polynomial of the knot is: -320*K1**4 - 352*K1**2*K2**2 + 880*K1**2*K2 - 240*K1**2*K3**2 - 1504*K1**2 + 32*K1*K2*K3**3 + 2224*K1*K2*K3 + 472*K1*K3*K4 + 24*K1*K4*K5 + 40*K1*K5*K6 - 88*K2**4 - 256*K2**2*K3**2 + 112*K2**2*K4 - 8*K2**2*K6**2 - 1480*K2**2 + 624*K2*K3*K5 + 40*K2*K4*K6 + 16*K2*K6*K8 - 304*K3**4 + 280*K3**2*K6 - 1328*K3**2 + 24*K3*K5*K8 - 244*K4**2 - 296*K5**2 - 112*K6**2 - 18*K8**2 + 1780
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.485']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71367', 'vk6.71428', 'vk6.71889', 'vk6.71950', 'vk6.72460', 'vk6.72600', 'vk6.72717', 'vk6.72822', 'vk6.72886', 'vk6.73028', 'vk6.74232', 'vk6.74384', 'vk6.74417', 'vk6.74860', 'vk6.75034', 'vk6.76606', 'vk6.76908', 'vk6.77024', 'vk6.77397', 'vk6.77769', 'vk6.77820', 'vk6.79276', 'vk6.79430', 'vk6.79749', 'vk6.79846', 'vk6.79876', 'vk6.80876', 'vk6.80905', 'vk6.81372', 'vk6.85517', 'vk6.87214', 'vk6.89254']
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 O1O2O3O4O5U1U3U5O6U4U2U6
R3 orbit {'O1O2O3O4O5U1U3U5O6U4U2U6'}
R3 orbit length 1
Gauss code of -K O1O2O3O4O5U6U4U2O6U1U3U5
Gauss code of K* O1O2O3U4O5O6O4U1U6U2U5U3
Gauss code of -K* O1O2O3U1O4O5O6U4U3U5U2U6
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 -4 0 -1 1 2 2],[ 4 0 4 1 3 2 2],[ 0 -4 0 -2 1 1 2],[ 1 -1 2 0 2 1 1],[-1 -3 -1 -2 0 0 1],[-2 -2 -1 -1 0 0 0],[-2 -2 -2 -1 -1 0 0]]
Primitive based matrix [[ 0 2 2 1 0 -1 -4],[-2 0 0 0 -1 -1 -2],[-2 0 0 -1 -2 -1 -2],[-1 0 1 0 -1 -2 -3],[ 0 1 2 1 0 -2 -4],[ 1 1 1 2 2 0 -1],[ 4 2 2 3 4 1 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-2,-1,0,1,4,0,0,1,1,2,1,2,1,2,1,2,3,2,4,1]
Phi over symmetry [-4,-1,0,1,2,2,1,4,3,2,2,2,2,1,1,1,1,2,0,1,0]
Phi of -K [-4,-1,0,1,2,2,2,0,2,4,4,-1,0,2,2,0,0,1,0,1,0]
Phi of K* [-2,-2,-1,0,1,4,0,0,0,2,4,1,1,2,4,0,0,2,-1,0,2]
Phi of -K* [-4,-1,0,1,2,2,1,4,3,2,2,2,2,1,1,1,1,2,0,1,0]
Symmetry type of based matrix c
u-polynomial t^4-2t^2
Normalized Jones-Krushkal polynomial 12z+25
Enhanced Jones-Krushkal polynomial -4w^3z+16w^2z+25w
Inner characteristic polynomial t^6+51t^4+25t^2
Outer characteristic polynomial t^7+77t^5+125t^3
Flat arrow polynomial -2*K1**2 - 2*K1*K3 + 2*K2 + K4 + 2
2-strand cable arrow polynomial -320*K1**4 - 352*K1**2*K2**2 + 880*K1**2*K2 - 240*K1**2*K3**2 - 1504*K1**2 + 32*K1*K2*K3**3 + 2224*K1*K2*K3 + 472*K1*K3*K4 + 24*K1*K4*K5 + 40*K1*K5*K6 - 88*K2**4 - 256*K2**2*K3**2 + 112*K2**2*K4 - 8*K2**2*K6**2 - 1480*K2**2 + 624*K2*K3*K5 + 40*K2*K4*K6 + 16*K2*K6*K8 - 304*K3**4 + 280*K3**2*K6 - 1328*K3**2 + 24*K3*K5*K8 - 244*K4**2 - 296*K5**2 - 112*K6**2 - 18*K8**2 + 1780
Genus of based matrix 1
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{5, 6}, {3, 4}, {1, 2}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {4, 5}, {2, 3}, {1}]]
If K is slice False
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