Knot table - ten crossings: Difference between revisions

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<noinclude>This is one of the tables included into [[The Rolfsen Knot Table]]</noinclude>
==Knots with 10 crossings==
==Knots with 10 crossings==
<center>
<center>
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{{Knot Table Image|10_6}}
{{Knot Table Image|10_6}}
{{Knot Table Image|10_7}}
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{{Knot Table Image|10_8}}
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{{Knot Table Image|10_9}}
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{{Knot Table Image|10_10}}
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{{Knot Table Image|10_11}}
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{{Knot Table Image|10_12}}
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{{Knot Table Image|10_13}}
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{{Knot Table Image|10_14}}
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{{Knot Table Image|10_15}}
{{Knot Table Image|10_15}}
{{Knot Table Image|10_16}}
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{{Knot Table Image|10_19}}
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{{Knot Table Image|10_20}}
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{{Knot Table Image|10_21}}
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{{Knot Table Image|10_21}}
{{Knot Table Image|10_22}}
{{Knot Table Image|10_22}}
{{Knot Table Image|10_23}}
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{{Knot Table Image|10_27}}
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{{Knot Table Image|10_28}}
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{{Knot Table Image|10_29}}
{{Knot Table Image|10_29}}
{{Knot Table Image|10_30}}
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{{Knot Table Image|10_31}}
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{{Knot Table Image|10_32}}
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{{Knot Table Image|10_36}}
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{{Knot Table Image|10_41}}
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{{Knot Table Image|10_44}}
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{{Knot Table Image|10_48}}
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{{Knot Table Image|10_50}}
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{{Knot Table Image|10_50}}
{{Knot Table Image|10_51}}
{{Knot Table Image|10_51}}
{{Knot Table Image|10_52}}
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{{Knot Table Image|10_55}}
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{{Knot Table Image|10_57}}
{{Knot Table Image|10_57}}
{{Knot Table Image|10_58}}
{{Knot Table Image|10_58}}
{{Knot Table Image|10_59}}
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{{Knot Table Image|10_60}}
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{{Knot Table Image|10_61}}
{{Knot Table Image|10_61}}
{{Knot Table Image|10_62}}
{{Knot Table Image|10_62}}
{{Knot Table Image|10_63}}
{{Knot Table Image|10_63}}
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{{Knot Table Image|10_64}}
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{{Knot Table Image|10_65}}
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{{Knot Table Image|10_78}}
{{Knot Table Image|10_78}}
{{Knot Table Image|10_79}}
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{{Knot Table Image|10_81}}
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{{Knot Table Image|10_82}}
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{{Knot Table Image|10_101}}
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{{Knot Table Image|10_102}}
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{{Knot Table Image|10_127}}
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{{Knot Table Image|10_128}}
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{{Knot Table Image|10_129}}
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{{Knot Table Image|10_130}}
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{{Knot Table Image|10_131}}
{{Knot Table Image|10_131}}
{{Knot Table Image|10_132}}
{{Knot Table Image|10_132}}
{{Knot Table Image|10_133}}
{{Knot Table Image|10_133}}
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{{Knot Table Image|10_134}}
{{Knot Table Image|10_134}}
{{Knot Table Image|10_135}}
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{{Knot Table Image|10_146}}
{{Knot Table Image|10_146}}
{{Knot Table Image|10_147}}
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{{Knot Table Image|10_148}}
{{Knot Table Image|10_148}}
{{Knot Table Image|10_149}}
{{Knot Table Image|10_149}}
{{Knot Table Image|10_150}}
{{Knot Table Image|10_150}}
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{{Knot Table Image|10_151}}
{{Knot Table Image|10_151}}
{{Knot Table Image|10_152}}
{{Knot Table Image|10_152}}
{{Knot Table Image|10_153}}
{{Knot Table Image|10_153}}
{{Knot Table Image|10_154}}
{{Knot Table Image|10_154}}
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{{Knot Table Image|10_155}}
{{Knot Table Image|10_155}}
{{Knot Table Image|10_156}}
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{{Knot Table Image|10_159}}
{{Knot Table Image|10_159}}
{{Knot Table Image|10_160}}
{{Knot Table Image|10_160}}
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{{Knot Table Image|10_161}}
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|-
⚫
{{Knot Table Image|10_161}}
|Where's<br>Perko?
|align=center|See<br><font color=red>warning</font><br>below
{{Knot Table Image|10_162}}
{{Knot Table Image|10_162}}
{{Knot Table Image|10_163}}
{{Knot Table Image|10_163}}
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</center>
</center>


In 1974 K. Perko noticed that the knots labeled 10<sub>161</sub> and 10<sub>162</sub> in Rolfsen's tables are in fact the same. In our table we removed his 10<sub>162</sub> and renumbered the subsequent knots, so that our 10 crossings total is 165, one less than Rolfsen's 166. Read more: [http://mathworld.wolfram.com/PerkoPair.html] [http://www.math.cuhk.edu.hk/publect/lecture4/perko.html] [http://www.maths.warwick.ac.uk/~bjs/Perko-page.html] [http://www.math.uiuc.edu/~jms/Videos/ke/images.html].
<font size=+1 color=red>'''Warning.'''</font> In 1973 K. Perko noticed that the knots that were later labeled 10<sub>161</sub> and 10<sub>162</sub> in Rolfsen's tables (which were published in 1976 and were based on earlier tables by Little (1900) and Conway (1970)) are in fact the same. In our table we removed Rolfsen's 10<sub>162</sub> and renumbered the subsequent knots, so that our 10 crossings total is 165, one less than Rolfsen's 166. Read more: [http://mathworld.wolfram.com/PerkoPair.html] [http://www.math.cuhk.edu.hk/publect/lecture4/perko.html] [http://www.maths.warwick.ac.uk/~bjs/Perko-page.html] [http://www.math.uiuc.edu/~jms/Videos/ke/images.html]
[http://knotplot.com/perko/].

Latest revision as of 10:04, 12 August 2013

This is one of the tables included into The Rolfsen Knot Table

Knots with 10 crossings

10 1.gif

10_1

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10_2

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10_161

See
warning
below

10 162.gif

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10 163.gif

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10 164.gif

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10 165.gif

10_165

Warning. In 1973 K. Perko noticed that the knots that were later labeled 10161 and 10162 in Rolfsen's tables (which were published in 1976 and were based on earlier tables by Little (1900) and Conway (1970)) are in fact the same. In our table we removed Rolfsen's 10162 and renumbered the subsequent knots, so that our 10 crossings total is 165, one less than Rolfsen's 166. Read more: [1] [2] [3] [4] [5].

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