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Flat knot 6.92

Min(phi) over symmetries of the knot is: [-4,-2,0,2,2,2,0,3,2,3,4,2,1,2,2,1,1,1,0,-1,-1]
Flat knots (up to 7 crossings) with same phi are :['6.92']
Arrow polynomial of the knot is: 4*K1**2*K2 - 4*K1**2 - 2*K2**2 + 3
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.92', '6.348', '6.490', '6.494']
Outer characteristic polynomial of the knot is: t^7+88t^5+56t^3
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.92']
2-strand cable arrow polynomial of the knot is: -32*K2**4*K4**2 + 128*K2**4*K4 - 672*K2**4 + 32*K2**2*K4**3 - 240*K2**2*K4**2 + 944*K2**2*K4 - 276*K2**2 + 144*K2*K4*K6 - 8*K4**4 - 312*K4**2 - 28*K6**2 + 318
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.92']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.70470', 'vk6.70485', 'vk6.70534', 'vk6.70614', 'vk6.70646', 'vk6.70670', 'vk6.70766', 'vk6.70849', 'vk6.70926', 'vk6.70955', 'vk6.71011', 'vk6.71119', 'vk6.71160', 'vk6.71175', 'vk6.71249', 'vk6.71305', 'vk6.72390', 'vk6.72405', 'vk6.72739', 'vk6.73050', 'vk6.73212', 'vk6.73246', 'vk6.73247', 'vk6.73609', 'vk6.74400', 'vk6.75131', 'vk6.75134', 'vk6.75358', 'vk6.75391', 'vk6.76486', 'vk6.76696', 'vk6.77727', 'vk6.78070', 'vk6.78095', 'vk6.78099', 'vk6.78105', 'vk6.78352', 'vk6.79345', 'vk6.79444', 'vk6.80800', 'vk6.85077', 'vk6.85604', 'vk6.85767', 'vk6.87177', 'vk6.87313', 'vk6.90128', 'vk6.90153', 'vk6.90193']
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 O1O2O3O4O5O6U2U5U6U1U4U3
R3 orbit {'O1O2O3O4O5O6U2U5U6U1U4U3', 'O1O2O3O4O5U1U4O6U2U5U6U3', 'O1O2O3O4O5U1O6U5U2U6U4U3'}
R3 orbit length 3
Gauss code of -K O1O2O3O4O5O6U4U3U6U1U2U5
Gauss code of K* O1O2O3O4O5O6U4U1U6U5U2U3
Gauss code of -K* O1O2O3O4O5O6U4U5U2U1U6U3
Diagrammatic symmetry type c
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 -4 2 2 0 2],[ 2 0 -2 3 2 0 2],[ 4 2 0 4 3 1 2],[-2 -3 -4 0 0 -1 1],[-2 -2 -3 0 0 -1 1],[ 0 0 -1 1 1 0 1],[-2 -2 -2 -1 -1 -1 0]]
Primitive based matrix [[ 0 2 2 2 0 -2 -4],[-2 0 1 0 -1 -2 -3],[-2 -1 0 -1 -1 -2 -2],[-2 0 1 0 -1 -3 -4],[ 0 1 1 1 0 0 -1],[ 2 2 2 3 0 0 -2],[ 4 3 2 4 1 2 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-2,-2,0,2,4,-1,0,1,2,3,1,1,2,2,1,3,4,0,1,2]
Phi over symmetry [-4,-2,0,2,2,2,0,3,2,3,4,2,1,2,2,1,1,1,0,-1,-1]
Phi of -K [-4,-2,0,2,2,2,0,3,2,3,4,2,1,2,2,1,1,1,0,-1,-1]
Phi of K* [-2,-2,-2,0,2,4,-1,-1,1,2,4,0,1,1,2,1,2,3,2,3,0]
Phi of -K* [-4,-2,0,2,2,2,2,1,2,3,4,0,2,2,3,1,1,1,-1,-1,0]
Symmetry type of based matrix c
u-polynomial t^4-2t^2
Normalized Jones-Krushkal polynomial 5z^2+14z+9
Enhanced Jones-Krushkal polynomial 5w^3z^2+14w^2z+9
Inner characteristic polynomial t^6+56t^4+8t^2
Outer characteristic polynomial t^7+88t^5+56t^3
Flat arrow polynomial 4*K1**2*K2 - 4*K1**2 - 2*K2**2 + 3
2-strand cable arrow polynomial -32*K2**4*K4**2 + 128*K2**4*K4 - 672*K2**4 + 32*K2**2*K4**3 - 240*K2**2*K4**2 + 944*K2**2*K4 - 276*K2**2 + 144*K2*K4*K6 - 8*K4**4 - 312*K4**2 - 28*K6**2 + 318
Genus of based matrix 1
Fillings of based matrix [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {4}, {2, 3}, {1}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {2, 5}, {1, 4}, {3}]]
If K is slice False
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