<p><a href="https://en.wikipedia.org/wiki/Composition_(number_theory)" class="extiw" title="w:Composition (number theory)">Compositions</a> of a number <i>n</i> correspond to <i>n-1</i> digit <a href="https://en.wikipedia.org/wiki/binary_numeral_system" class="extiw" title="w:binary numeral system">binary numbers</a>.
</p><p><b>Left cube:</b> 3 digit binary numbers
</p><p><b>Central cube:</b> <a href="https://en.wikipedia.org/wiki/Logical_matrix" class="extiw" title="w:Logical matrix">Logical matrices</a> of <a href="https://en.wikipedia.org/wiki/equivalence_relation" class="extiw" title="w:equivalence relation">equivalence relations</a> as in <a href="//commons.wikimedia.org/wiki/File:Set_partitions_4;_Hasse;_matrices.svg" class="image"><img alt="Set partitions 4; Hasse; matrices.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Set_partitions_4%3B_Hasse%3B_matrices.svg/200px-Set_partitions_4%3B_Hasse%3B_matrices.svg.png" decoding="async" width="200" height="232" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Set_partitions_4%3B_Hasse%3B_matrices.svg/300px-Set_partitions_4%3B_Hasse%3B_matrices.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Set_partitions_4%3B_Hasse%3B_matrices.svg/400px-Set_partitions_4%3B_Hasse%3B_matrices.svg.png 2x" data-file-width="630" data-file-height="732"></a>
</p><p><b>Right cube:</b> Compositions
</p>
<div class="center"><div class="thumb tnone"><div class="thumbinner" style="width:602px;"><a href="//commons.wikimedia.org/wiki/File:Binary_and_compositions_5.svg" class="image"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Binary_and_compositions_5.svg/600px-Binary_and_compositions_5.svg.png" decoding="async" width="600" height="186" class="thumbimage" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Binary_and_compositions_5.svg/900px-Binary_and_compositions_5.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Binary_and_compositions_5.svg/1200px-Binary_and_compositions_5.svg.png 2x" data-file-width="1160" data-file-height="360"></a>  <div class="thumbcaption"><div class="magnify"><a href="//commons.wikimedia.org/wiki/File:Binary_and_compositions_5.svg" class="internal" title="Enlarge"></a></div>The same with 4 bit binary numbers and compositions of 5</div></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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2010
<span class="int-own-work" lang="en">Own work</span>