10 55
From Knot Atlas
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See the full Rolfsen Knot Table. Visit 10 55's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X1425 X3849 X5,12,6,13 X15,18,16,19 X9,16,10,17 X17,10,18,11 X13,20,14,1 X19,14,20,15 X11,6,12,7 X7283 |
Gauss code | -1, 10, -2, 1, -3, 9, -10, 2, -5, 6, -9, 3, -7, 8, -4, 5, -6, 4, -8, 7 |
Dowker-Thistlethwaite code | 4 8 12 2 16 6 20 18 10 14 |
Conway Notation | [23,21,2] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 12, width is 5, Braid index is 5 |
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![]() [{13, 5}, {4, 11}, {9, 12}, {11, 13}, {10, 6}, {5, 9}, {6, 3}, {2, 4}, {3, 1}, {7, 10}, {8, 2}, {12, 7}, {1, 8}] |
[edit Notes on presentations of 10 55]
Three dimensional invariants
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Four dimensional invariants
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Polynomial invariants
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, ): {}
Vassiliev invariants
V2 and V3: | (5, -10) |
V2,1 through V6,9: |
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V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where -4 is the signature of 10 55. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
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Integral Khovanov Homology
(db, data source) |
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