<p><a href="https://en.wikipedia.org/wiki/Permutohedron" class="extiw" title="w:Permutohedron">Permutohedron</a> of the symmetric group <a href="https://en.wikiversity.org/wiki/Symmetric_group_S4" class="extiw" title="v:Symmetric group S4">S4</a>
</p>
The permutations are represented by their <a href="https://en.wikipedia.org/wiki/Inversion_(discrete_mathematics)" class="extiw" title="w:Inversion (discrete mathematics)">inversion</a> sets, which are subsets of the set containing these six elements:<a href="//commons.wikimedia.org/wiki/File:2-element_subsets_of_4_elements;_array,_hexagonal.svg" class="image"><img alt="2-element subsets of 4 elements; array, hexagonal.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/2-element_subsets_of_4_elements%3B_array%2C_hexagonal.svg/100px-2-element_subsets_of_4_elements%3B_array%2C_hexagonal.svg.png" decoding="async" width="100" height="97" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/2-element_subsets_of_4_elements%3B_array%2C_hexagonal.svg/150px-2-element_subsets_of_4_elements%3B_array%2C_hexagonal.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/2-element_subsets_of_4_elements%3B_array%2C_hexagonal.svg/200px-2-element_subsets_of_4_elements%3B_array%2C_hexagonal.svg.png 2x" data-file-width="298" data-file-height="289"></a>
<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>
</td>
<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>
</td></tr></tbody></table>
CC BY 3.0
<span class="int-own-work" lang="en">Own work</span>