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Flat knot 6.1214

Min(phi) over symmetries of the knot is: [-2,-2,0,0,2,2,-1,0,1,2,3,0,1,1,2,0,1,1,2,2,-1]
Flat knots (up to 7 crossings) with same phi are :['6.1214']
Arrow polynomial of the knot is: 8*K1**2*K2 - 8*K1**2 - 4*K2**2 + 5
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.89', '6.1214', '6.1929']
Outer characteristic polynomial of the knot is: t^7+48t^5+44t^3
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1214']
2-strand cable arrow polynomial of the knot is: -64*K2**4*K4**2 + 256*K2**4*K4 - 1280*K2**4 + 128*K2**2*K4**3 - 800*K2**2*K4**2 + 2528*K2**2*K4 - 1168*K2**2 + 496*K2*K4*K6 - 48*K4**4 - 904*K4**2 - 96*K6**2 + 950
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1214']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.72503', 'vk6.72504', 'vk6.72506', 'vk6.72551', 'vk6.72554', 'vk6.72559', 'vk6.72564', 'vk6.72934', 'vk6.72937', 'vk6.72941', 'vk6.72972', 'vk6.72973', 'vk6.77824', 'vk6.77832', 'vk6.77835', 'vk6.77838', 'vk6.77842', 'vk6.77850', 'vk6.87264', 'vk6.90145']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is r.
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 O1O2O3O4U2U5U4O6O5U1U6U3
R3 orbit {'O1O2O3O4U2U5U4O6O5U1U6U3'}
R3 orbit length 1
Gauss code of -K Same
Gauss code of K* O1O2O3U4U2O5O4O6U5U1U6U3
Gauss code of -K* O1O2O3U4U2O5O4O6U5U1U6U3
Diagrammatic symmetry type r
Flat genus of the diagram 2
If K is checkerboard colorable True
If K is almost classical False
Based matrix from Gauss code [[ 0 -2 -2 2 2 0 0],[ 2 0 -1 3 2 1 0],[ 2 1 0 2 1 1 0],[-2 -3 -2 0 1 -2 -1],[-2 -2 -1 -1 0 -2 -1],[ 0 -1 -1 2 2 0 0],[ 0 0 0 1 1 0 0]]
Primitive based matrix [[ 0 2 2 0 0 -2 -2],[-2 0 1 -1 -2 -2 -3],[-2 -1 0 -1 -2 -1 -2],[ 0 1 1 0 0 0 0],[ 0 2 2 0 0 -1 -1],[ 2 2 1 0 1 0 1],[ 2 3 2 0 1 -1 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-2,0,0,2,2,-1,1,2,2,3,1,2,1,2,0,0,0,1,1,-1]
Phi over symmetry [-2,-2,0,0,2,2,-1,0,1,2,3,0,1,1,2,0,1,1,2,2,-1]
Phi of -K [-2,-2,0,0,2,2,-1,1,2,2,3,1,2,1,2,0,0,0,1,1,-1]
Phi of K* [-2,-2,0,0,2,2,-1,0,1,2,3,0,1,1,2,0,1,1,2,2,-1]
Phi of -K* [-2,-2,0,0,2,2,-1,0,1,2,3,0,1,1,2,0,1,1,2,2,-1]
Symmetry type of based matrix r
u-polynomial 0
Normalized Jones-Krushkal polynomial 7z^2+20z+13
Enhanced Jones-Krushkal polynomial 7w^3z^2+20w^2z+13
Inner characteristic polynomial t^6+32t^4+12t^2
Outer characteristic polynomial t^7+48t^5+44t^3
Flat arrow polynomial 8*K1**2*K2 - 8*K1**2 - 4*K2**2 + 5
2-strand cable arrow polynomial -64*K2**4*K4**2 + 256*K2**4*K4 - 1280*K2**4 + 128*K2**2*K4**3 - 800*K2**2*K4**2 + 2528*K2**2*K4 - 1168*K2**2 + 496*K2*K4*K6 - 48*K4**4 - 904*K4**2 - 96*K6**2 + 950
Genus of based matrix 1
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {2, 4}, {1, 3}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}]]
If K is slice False
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