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Flat knot 6.108

Min(phi) over symmetries of the knot is: [-4,1,1,2,2,3,2,0,1,1]
Flat knots (up to 7 crossings) with same phi are :['6.108']
Arrow polynomial of the knot is: -4*K1*K2 - 2*K1*K3 + 2*K1 + K2 + 2*K3 + K4 + 1
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.108', '6.157', '6.283', '6.399', '6.445', '6.510']
Outer characteristic polynomial of the knot is: t^5+51t^3+5t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.108']
2-strand cable arrow polynomial of the knot is: -240*K1**4 + 192*K1**3*K2*K3 - 448*K1**2*K2**2 + 432*K1**2*K2 - 208*K1**2*K3**2 - 32*K1**2*K4**2 - 32*K1**2*K5**2 - 472*K1**2 + 648*K1*K2*K3 + 312*K1*K3*K4 + 224*K1*K4*K5 + 80*K1*K5*K6 - 48*K2**2*K4**2 + 320*K2**2*K4 - 48*K2**2*K5**2 - 8*K2**2*K6**2 - 808*K2**2 + 368*K2*K3*K5 + 96*K2*K4*K6 + 32*K2*K5*K7 + 8*K2*K6*K8 + 24*K3**2*K6 - 524*K3**2 - 398*K4**2 - 304*K5**2 - 80*K6**2 - 4*K7**2 - 2*K8**2 + 918
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.108']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4706', 'vk6.5013', 'vk6.6212', 'vk6.6677', 'vk6.8199', 'vk6.8622', 'vk6.9575', 'vk6.9912', 'vk6.16684', 'vk6.19082', 'vk6.19129', 'vk6.19268', 'vk6.19560', 'vk6.22518', 'vk6.22997', 'vk6.23114', 'vk6.23571', 'vk6.23908', 'vk6.25707', 'vk6.26079', 'vk6.26453', 'vk6.28416', 'vk6.29922', 'vk6.29971', 'vk6.30081', 'vk6.35109', 'vk6.37811', 'vk6.40094', 'vk6.40344', 'vk6.44669', 'vk6.46802', 'vk6.48057', 'vk6.48740', 'vk6.49747', 'vk6.51631', 'vk6.51735', 'vk6.56597', 'vk6.59327', 'vk6.64866', 'vk6.66191']
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 O1O2O3O4O5O6U2U6U5U4U1U3
R3 orbit {'O1O2O3O4O5U1U5U4U6U2O6U3', 'O1O2O3O4O5O6U2U6U5U4U1U3'}
R3 orbit length 2
Gauss code of -K O1O2O3O4O5O6U4U6U3U2U1U5
Gauss code of K* O1O2O3O4O5O6U5U1U6U4U3U2
Gauss code of -K* O1O2O3O4O5O6U5U4U3U1U6U2
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 -1 -4 2 1 1 1],[ 1 0 -3 2 1 1 1],[ 4 3 0 4 3 2 1],[-2 -2 -4 0 0 0 0],[-1 -1 -3 0 0 0 0],[-1 -1 -2 0 0 0 0],[-1 -1 -1 0 0 0 0]]
Primitive based matrix [[ 0 2 1 1 -4],[-2 0 0 0 -4],[-1 0 0 0 -2],[-1 0 0 0 -3],[ 4 4 2 3 0]]
If based matrix primitive False
Phi of primitive based matrix [-2,-1,-1,4,0,0,4,0,2,3]
Phi over symmetry [-4,1,1,2,2,3,2,0,1,1]
Phi of -K [-4,1,1,2,2,3,2,0,1,1]
Phi of K* [-2,-1,-1,4,1,1,2,0,2,3]
Phi of -K* [-4,1,1,2,2,3,4,0,0,0]
Symmetry type of based matrix c
u-polynomial t^4-t^2-2t
Normalized Jones-Krushkal polynomial 5z+11
Enhanced Jones-Krushkal polynomial -8w^3z+13w^2z+11w
Inner characteristic polynomial t^4+29t^2
Outer characteristic polynomial t^5+51t^3+5t
Flat arrow polynomial -4*K1*K2 - 2*K1*K3 + 2*K1 + K2 + 2*K3 + K4 + 1
2-strand cable arrow polynomial -240*K1**4 + 192*K1**3*K2*K3 - 448*K1**2*K2**2 + 432*K1**2*K2 - 208*K1**2*K3**2 - 32*K1**2*K4**2 - 32*K1**2*K5**2 - 472*K1**2 + 648*K1*K2*K3 + 312*K1*K3*K4 + 224*K1*K4*K5 + 80*K1*K5*K6 - 48*K2**2*K4**2 + 320*K2**2*K4 - 48*K2**2*K5**2 - 8*K2**2*K6**2 - 808*K2**2 + 368*K2*K3*K5 + 96*K2*K4*K6 + 32*K2*K5*K7 + 8*K2*K6*K8 + 24*K3**2*K6 - 524*K3**2 - 398*K4**2 - 304*K5**2 - 80*K6**2 - 4*K7**2 - 2*K8**2 + 918
Genus of based matrix 1
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {5}, {2, 4}, {3}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {5}, {3}, {1, 2}]]
If K is slice False
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