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<h1 class="title">Known necktie knots</h1>
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<p>Mikael Vejdemo-Johansson </p>
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<section id="known-named-tieknots-and-their-knotting-sequences" class="level1">
<h1>Known named tieknots and their knotting sequences</h1>
<table class="table">
<thead>
<tr class="header">
<th style="text-align: left;">Tie knot name</th>
<th style="text-align: left;">RLC-sequence</th>
<th style="text-align: left;">WT-sequence</th>
<th style="text-align: left;">Fink and Mao index</th>
<th style="text-align: left;">H-P-S-VJ-index</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">Oriental</td>
<td style="text-align: left;">LRCU</td>
<td style="text-align: left;">WWU</td>
<td style="text-align: left;">1</td>
<td style="text-align: left;">C-1</td>
</tr>
<tr class="even">
<td style="text-align: left;">4-in-hand</td>
<td style="text-align: left;">LRLCU</td>
<td style="text-align: left;">WTTU</td>
<td style="text-align: left;">2</td>
<td style="text-align: left;">C-2</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Kelvin</td>
<td style="text-align: left;">LRLRCU</td>
<td style="text-align: left;">WTWWU</td>
<td style="text-align: left;">3</td>
<td style="text-align: left;">C-5</td>
</tr>
<tr class="even">
<td style="text-align: left;">Nicky</td>
<td style="text-align: left;">LCRLCU</td>
<td style="text-align: left;">TTTTU</td>
<td style="text-align: left;">4</td>
<td style="text-align: left;">C-3</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Pratt/Shelby</td>
<td style="text-align: left;">LCLRCU</td>
<td style="text-align: left;">TWWWU</td>
<td style="text-align: left;">5</td>
<td style="text-align: left;">C-4</td>
</tr>
<tr class="even">
<td style="text-align: left;">Victoria</td>
<td style="text-align: left;">LRLRLCU</td>
<td style="text-align: left;">WTWTTU</td>
<td style="text-align: left;">6</td>
<td style="text-align: left;">C-8</td>
</tr>
<tr class="odd">
<td style="text-align: left;">half-Windsor</td>
<td style="text-align: left;">LRCLRCU</td>
<td style="text-align: left;">WWWWWU</td>
<td style="text-align: left;">7</td>
<td style="text-align: left;">C-10</td>
</tr>
<tr class="even">
<td style="text-align: left;">co-half-Windsor</td>
<td style="text-align: left;">LRCRLCU</td>
<td style="text-align: left;">WWTTTU</td>
<td style="text-align: left;">8</td>
<td style="text-align: left;">C-9</td>
</tr>
<tr class="odd">
<td style="text-align: left;">St Andrew</td>
<td style="text-align: left;">LRLCRLCU</td>
<td style="text-align: left;">WWWWTTU</td>
<td style="text-align: left;">12</td>
<td style="text-align: left;">C-21</td>
</tr>
<tr class="even">
<td style="text-align: left;">co-St Andrew</td>
<td style="text-align: left;">LRLCLRCU</td>
<td style="text-align: left;">WWTTWWU</td>
<td style="text-align: left;">14</td>
<td style="text-align: left;">C-20</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Plattsburgh</td>
<td style="text-align: left;">LCRCLRCU</td>
<td style="text-align: left;">TTWTTTU</td>
<td style="text-align: left;">18</td>
<td style="text-align: left;">C-12</td>
</tr>
<tr class="even">
<td style="text-align: left;">co-Plattsburgh</td>
<td style="text-align: left;">LCRCRLCU</td>
<td style="text-align: left;">TWTTTTU</td>
<td style="text-align: left;">19</td>
<td style="text-align: left;">C-13</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Cavendish</td>
<td style="text-align: left;">LRLCRLRCU</td>
<td style="text-align: left;">WTWWWWWU</td>
<td style="text-align: left;">23</td>
<td style="text-align: left;">C-39</td>
</tr>
<tr class="even">
<td style="text-align: left;">Christensen</td>
<td style="text-align: left;">LRCLRLRCUU</td>
<td style="text-align: left;">WTWWTTTU</td>
<td style="text-align: left;">25</td>
<td style="text-align: left;">C-34</td>
</tr>
<tr class="odd">
<td style="text-align: left;">co-Christensen</td>
<td style="text-align: left;">LRCRLRLRCUU</td>
<td style="text-align: left;">TTTWTWWU</td>
<td style="text-align: left;">27</td>
<td style="text-align: left;">C-24</td>
</tr>
<tr class="even">
<td style="text-align: left;">Windsor</td>
<td style="text-align: left;">LCRLCRLCU</td>
<td style="text-align: left;">TWWWWWWU</td>
<td style="text-align: left;">31</td>
<td style="text-align: left;">C-38</td>
</tr>
<tr class="odd">
<td style="text-align: left;">co-Windsor 1 (Novotny calls this Persian)</td>
<td style="text-align: left;">LCLRCLRCU</td>
<td style="text-align: left;">TTTTWWWU</td>
<td style="text-align: left;">32</td>
<td style="text-align: left;">C-23</td>
</tr>
<tr class="even">
<td style="text-align: left;">co-Windsor 2</td>
<td style="text-align: left;">LCRLCLRCU</td>
<td style="text-align: left;">WWWTTTTU</td>
<td style="text-align: left;">33</td>
<td style="text-align: left;">C-37</td>
</tr>
<tr class="odd">
<td style="text-align: left;">co-Windsor 3</td>
<td style="text-align: left;">LCLRCRLCU</td>
<td style="text-align: left;">WWTWWWWU</td>
<td style="text-align: left;">35</td>
<td style="text-align: left;">C-40</td>
</tr>
<tr class="even">
<td style="text-align: left;">Granchester</td>
<td style="text-align: left;">LRLRCLRLCU</td>
<td style="text-align: left;">WTTTTWTTU</td>
<td style="text-align: left;">44</td>
<td style="text-align: left;">C-54</td>
</tr>
<tr class="odd">
<td style="text-align: left;">co-Granchester</td>
<td style="text-align: left;">LRLRCRLRCU</td>
<td style="text-align: left;">WTTWWTWWU</td>
<td style="text-align: left;">48</td>
<td style="text-align: left;">C-72</td>
</tr>
<tr class="even">
<td style="text-align: left;">Hanover</td>
<td style="text-align: left;">LRCLRCLRCU</td>
<td style="text-align: left;">WWTTTTTTU</td>
<td style="text-align: left;">54</td>
<td style="text-align: left;">C-58</td>
</tr>
<tr class="odd">
<td style="text-align: left;">co-Hanover 1</td>
<td style="text-align: left;">LRCRLCRLCU</td>
<td style="text-align: left;">WWWWWTTTU</td>
<td style="text-align: left;">55</td>
<td style="text-align: left;">C-84</td>
</tr>
<tr class="even">
<td style="text-align: left;">co-Hanover 2</td>
<td style="text-align: left;">LRCLRCRLCU</td>
<td style="text-align: left;">TTTWWWWWU</td>
<td style="text-align: left;">56</td>
<td style="text-align: left;">C-59</td>
</tr>
<tr class="odd">
<td style="text-align: left;">co-Hanover 3</td>
<td style="text-align: left;">LCRLCRLRCU</td>
<td style="text-align: left;">WWTTTWWWU</td>
<td style="text-align: left;">58</td>
<td style="text-align: left;">C-77</td>
</tr>
<tr class="even">
<td style="text-align: left;">Balthus</td>
<td style="text-align: left;">LCRCLCRLCU</td>
<td style="text-align: left;">TWTTWWWWU</td>
<td style="text-align: left;">78</td>
<td style="text-align: left;">C-63</td>
</tr>
<tr class="odd">
<td style="text-align: left;">co-Balthus</td>
<td style="text-align: left;">LCRCLCLRCU</td>
<td style="text-align: left;">TWTTWTTTU</td>
<td style="text-align: left;">81</td>
<td style="text-align: left;">C-51</td>
</tr>
<tr class="even">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=qFdk-IT2cmg">Edeity</a> aka Merovingian</td>
<td style="text-align: left;">LCLRCRLCU</td>
<td style="text-align: left;">TWWWTTTU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">C-30</td>
</tr>
<tr class="odd">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=2Ioxajtj2gA">Trinity</a></td>
<td style="text-align: left;">LCLRCRLCURLU</td>
<td style="text-align: left;">TWWWTTTUTTU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">L-110</td>
</tr>
<tr class="even">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=gKs7WwrEaIs">Eldredge</a></td>
<td style="text-align: left;">LCRLRCRLUCRCLU</td>
<td style="text-align: left;">TTTWWTTUTTWWU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">L-373</td>
</tr>
<tr class="odd">
<td style="text-align: left;"><a href="http://fairyfrog.deviantart.com/art/The-Allwin-tie-knot-Tutorial-433909390">Allwin</a></td>
<td style="text-align: left;">LCLRCLRLRCUULRU</td>
<td style="text-align: left;">TWWWWWTWWUUWWU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">R-650</td>
</tr>
<tr class="even">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=gUVBQ00iwTI">Cape</a></td>
<td style="text-align: left;">LCRLRCRLCU</td>
<td style="text-align: left;">TTTWWTTTU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">C-46</td>
</tr>
<tr class="odd">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=Hrgu75j-Llw">Truelove</a></td>
<td style="text-align: left;">RCRLCRLCUCRUUU</td>
<td style="text-align: left;">Not a T/W-knot</td>
<td style="text-align: left;"></td>
<td style="text-align: left;"></td>
</tr>
<tr class="even">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=Lot7tq1Valo">Murrell</a> (thin end Windsor)</td>
<td style="text-align: left;">LCLRCLRCU</td>
<td style="text-align: left;">TWWWWWWU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">C-38</td>
</tr>
<tr class="odd">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=KBd8bRbRISo">Atlantic</a></td>
<td style="text-align: left;">LCRLCU</td>
<td style="text-align: left;">TTTTU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">C-3</td>
</tr>
<tr class="even">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=QVo5V3D_C6Y">Novotny</a></td>
<td style="text-align: left;">LCRLRCLRUCLCRU</td>
<td style="text-align: left;">TTTWWWWUWWTTU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">R-451</td>
</tr>
<tr class="odd">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=z5sWQNWzsCk">Floating Spiral</a> (odd mid-tuck)</td>
<td style="text-align: left;">LRLRLRUCU</td>
<td style="text-align: left;">WTWTWUWU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">C-19</td>
</tr>
<tr class="even">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=YBsIQZ3GOoY">Van Wijk</a></td>
<td style="text-align: left;">LRLRLRLCUUU</td>
<td style="text-align: left;">WTWTWTTUUU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">C-33</td>
</tr>
<tr class="odd">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=Q5-Np9zDADE">Taurus</a> (broad blade)</td>
<td style="text-align: left;">LCLRCU.UULCU</td>
<td style="text-align: left;">TWWWU.UUTTU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">L-15</td>
</tr>
<tr class="even">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=8SocEpK0b4I">Fishbone</a></td>
<td style="text-align: left;">LCRLCRCLCRCLCRU</td>
<td style="text-align: left;">TTTTTWWTTWWTTU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;"></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=J22PLA6e7UY">Rose knot</a></td>
<td style="text-align: left;">LCRLRCLRUCLU</td>
<td style="text-align: left;">TTTWWWWUWWU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">L-128</td>
</tr>
<tr class="even">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=nbnbYYpYkgo">Ellieknot</a> (backside tuck)</td>
<td style="text-align: left;">LCRLRCLRCLCRCU</td>
<td style="text-align: left;">TTTWWWWWWTTWU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;"></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=n8mGf5JN4Xc">Boutonniere</a> (no tuck)</td>
<td style="text-align: left;">LCRLCRCLCRCLCRCLCR</td>
<td style="text-align: left;">TTTTTWWTTWWTTWWTT</td>
<td style="text-align: left;"></td>
<td style="text-align: left;"></td>
</tr>
<tr class="even">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=b6dD3nokKn8">Capsule</a></td>
<td style="text-align: left;">LCRLRCRLCRUU'U</td>
<td style="text-align: left;">TTTWWTTTTUU'U</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">R-92</td>
</tr>
<tr class="odd">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=ugVkQfzRfIs">Eric Glennie Braided</a> (backside tuck)</td>
<td style="text-align: left;">LCRLCRUCU</td>
<td style="text-align: left;">TTTTTUWU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;"></td>
</tr>
<tr class="even">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=6Anx_uIadJc">Four Rings</a> (backside tuck)</td>
<td style="text-align: left;">LCRLU'UUCU</td>
<td style="text-align: left;">TTTU'UUTU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">C-3</td>
</tr>
<tr class="odd">
<td style="text-align: left;"><a href="http://www.youtube.com/watch?v=RtdZFrVTONk">Diagonal</a> (broad blade, tuck goes downward, twist tie)</td>
<td style="text-align: left;">LRLRCLUU</td>
<td style="text-align: left;">WTWWWUU</td>
<td style="text-align: left;"></td>
<td style="text-align: left;">L-9</td>
</tr>
</tbody>
</table>
<p>Fink and Mao indices from <a href="http://www.tcm.phy.cam.ac.uk/~tmf20/tieknots.shtml">Tomas Fink's Encyclopedia of Tie Knots</a>.<br>
Hirsh-Patterson-Sandberg-Vejdemo Johansson-indices from <a href="http://arxiv.org/abs/1401.8242">More Ties than we thought</a>.</p>
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