10 85
From Knot Atlas
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See the full Rolfsen Knot Table. Visit 10 85's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X6271 X16,6,17,5 X18,11,19,12 X14,7,15,8 X8394 X4,9,5,10 X20,13,1,14 X10,17,11,18 X12,19,13,20 X2,16,3,15 |
Gauss code | 1, -10, 5, -6, 2, -1, 4, -5, 6, -8, 3, -9, 7, -4, 10, -2, 8, -3, 9, -7 |
Dowker-Thistlethwaite code | 6 8 16 14 4 18 20 2 10 12 |
Conway Notation | [.4.20] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||
Length is 10, width is 3, Braid index is 3 |
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![]() [{3, 12}, {2, 6}, {8, 13}, {9, 7}, {10, 8}, {11, 9}, {4, 10}, {6, 11}, {5, 3}, {12, 4}, {1, 5}, {13, 2}, {7, 1}] |
[edit Notes on presentations of 10 85]
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: | (2, -3) |
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 85. 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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