<div class="thumb tright"><div class="thumbinner" style="width:222px;"><a href="//commons.wikimedia.org/wiki/File:Symmetric_group_4;_permutohedron_3D;_l-e_factorial_numbers.svg" class="image"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Symmetric_group_4%3B_permutohedron_3D%3B_l-e_factorial_numbers.svg/220px-Symmetric_group_4%3B_permutohedron_3D%3B_l-e_factorial_numbers.svg.png" decoding="async" width="220" height="220" class="thumbimage" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Symmetric_group_4%3B_permutohedron_3D%3B_l-e_factorial_numbers.svg/330px-Symmetric_group_4%3B_permutohedron_3D%3B_l-e_factorial_numbers.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Symmetric_group_4%3B_permutohedron_3D%3B_l-e_factorial_numbers.svg/440px-Symmetric_group_4%3B_permutohedron_3D%3B_l-e_factorial_numbers.svg.png 2x" data-file-width="744" data-file-height="744"></a>  <div class="thumbcaption"><div class="magnify"><a href="//commons.wikimedia.org/wiki/File:Symmetric_group_4;_permutohedron_3D;_l-e_factorial_numbers.svg" class="internal" title="Enlarge"></a></div>Permutohedron with permutations as coordinates</div></div></div>
<p><a href="https://en.wikipedia.org/wiki/Permutohedron" class="extiw" title="w:Permutohedron">Permutohedron</a> of the <a href="https://en.wikipedia.org/wiki/symmetric_group" class="extiw" title="w:symmetric group">symmetric group</a> <a href="https://en.wikiversity.org/wiki/Symmetric_group_S4" class="extiw" title="v:Symmetric group S4">S<sub>4</sub></a>
</p><p>The vertices are labelled with the index numbers of the permutations shown in the file on the right.<br><small>E.g. (3, 1, 2, 4) has the index number 3. Compare <a href="//commons.wikimedia.org/wiki/File:Symmetric_group_4;_permutation_list.svg" title="File:Symmetric group 4; permutation list.svg">this list</a>.</small>
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<div class="thumb tleft"><div class="thumbinner" style="width:222px;"><a href="//commons.wikimedia.org/wiki/File:Symmetric_group_4;_permutohedron;_numbers.svg" class="image"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Symmetric_group_4%3B_permutohedron%3B_numbers.svg/220px-Symmetric_group_4%3B_permutohedron%3B_numbers.svg.png" decoding="async" width="220" height="220" class="thumbimage" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Symmetric_group_4%3B_permutohedron%3B_numbers.svg/330px-Symmetric_group_4%3B_permutohedron%3B_numbers.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Symmetric_group_4%3B_permutohedron%3B_numbers.svg/440px-Symmetric_group_4%3B_permutohedron%3B_numbers.svg.png 2x" data-file-width="744" data-file-height="744"></a>  <div class="thumbcaption"><div class="magnify"><a href="//commons.wikimedia.org/wiki/File:Symmetric_group_4;_permutohedron;_numbers.svg" class="internal" title="Enlarge"></a></div>Corresponding <a href="https://en.wikipedia.org/wiki/Schlegel_diagram" class="extiw" title="w:Schlegel diagram">Schlegel diagram</a></div></div></div>
<table><tbody><tr><td style="padding: 15px;"><a href="//commons.wikimedia.org/wiki/File:Watchduck.svg" class="image"><img alt="Watchduck.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/40px-Watchduck.svg.png" decoding="async" width="40" height="46" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/60px-Watchduck.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/80px-Watchduck.svg.png 2x" data-file-width="703" data-file-height="806"></a>
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<td><a href="//commons.wikimedia.org/wiki/User:Watchduck" title="User:Watchduck">Watchduck</a><br><span style="color: gray; font-size: 80%;">You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".</span>
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