<table class="wikitable" style="width: 100%;"><tbody><tr><th>Image set <a href="//commons.wikimedia.org/wiki/Category:Permutations_of_tesseract_vertices;_set_partitions" title="Category:Permutations of tesseract vertices; set partitions">Permutations of tesseract vertices; set partitions</a>
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<div class="thumb tright"><div class="thumbinner" style="width:302px;"><a href="//commons.wikimedia.org/wiki/File:16_choose_2_triangle_colored.svg" class="image"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/19/16_choose_2_triangle_colored.svg/300px-16_choose_2_triangle_colored.svg.png" decoding="async" width="300" height="270" class="thumbimage" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/1/19/16_choose_2_triangle_colored.svg/450px-16_choose_2_triangle_colored.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/1/19/16_choose_2_triangle_colored.svg/600px-16_choose_2_triangle_colored.svg.png 2x" data-file-width="1046" data-file-height="941"></a>  <div class="thumbcaption"><div class="magnify"><a href="//commons.wikimedia.org/wiki/File:16_choose_2_triangle_colored.svg" class="internal" title="Enlarge"></a></div>The pair (<i>a</i>, <i>b</i>) is in the ascending diagonal <i>a</i> and the descending diagonal <i>b</i>.</div></div></div>
<p><a href="https://en.wikipedia.org/wiki/Partition_of_a_set" class="extiw" title="w:Partition of a set">Set partition</a> of a pair of inverse permutations (or one self-inverse permutation) in the symmetry group of the tesseract
</p><p>The <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tbinom {16}{2}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mrow><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="1.2em" minsize="1.2em">(</mo></mrow><mfrac linethickness="0"><mn>16</mn><mn>2</mn></mfrac><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="1.2em" minsize="1.2em">)</mo></mrow></mrow></mstyle></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle {\tbinom {16}{2}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/114729401459308838a59fdd0e7607e516eb5f35" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:3.774ex; height:3.343ex;" alt="{\displaystyle {\tbinom {16}{2}}}"></span> = <a href="https://en.wikipedia.org/wiki/Triangular_number" class="extiw" title="w:Triangular number">120</a> hexagons correspond to the 2-element <a href="https://en.wikipedia.org/wiki/Subset" class="extiw" title="w:Subset">subsets</a> of a 16-element set.<br></p>
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