File:Hypercubeorder binary.svg
Summary
The 4D-<a href="https://en.wikipedia.org/wiki/en:hypercube" class="extiw" title="w:en:hypercube">hypercube</a>, layered according to distance from one corner.
As described in "Alice in Wonderland" by the <a href="https://en.wikipedia.org/wiki/en:Cheshire_Cat" class="extiw" title="w:en:Cheshire Cat">Cheshire Cat</a>, this vertex-first-shadow of the <a href="https://en.wikipedia.org/wiki/en:tesseract" class="extiw" title="w:en:tesseract">tesseract</a> forms a <a href="https://en.wikipedia.org/wiki/en:rhombic_dodecahedron" class="extiw" title="w:en:rhombic dodecahedron">rhombic dodecahedron</a>.
Note that the two central (green) vertices should coincide if using an orthogonal projection from 4 to 3 dimensions, but were drawn here slightly apart.
The eight <a href="https://en.wikipedia.org/wiki/en:nibble" class="extiw" title="w:en:nibble">nibbles</a> with <a href="https://en.wikipedia.org/wiki/en:Parity_(mathematics)" class="extiw" title="w:en:Parity (mathematics)">odd</a> <a href="https://en.wikipedia.org/wiki/en:binary" class="extiw" title="w:en:binary">binary</a> <a href="https://en.wikipedia.org/wiki/en:digit_sum" class="extiw" title="w:en:digit sum">digit sums</a> form a <a href="https://en.wikipedia.org/wiki/en:cube" class="extiw" title="w:en:cube">cube</a> and are marked in white.
The two pallindromes 0110 and 1001 (compare <a href="https://en.wikipedia.org/wiki/en:exclusive_or" class="extiw" title="w:en:exclusive or">XOR</a> and <a href="https://en.wikipedia.org/wiki/en:logical_bicontitional" class="extiw" title="w:en:logical bicontitional">XNOR</a>) are projected in the center of the rhombic dodecahedron and are marked in green.
The other six nibbles with <a href="https://en.wikipedia.org/wiki/en:Parity_(mathematics)" class="extiw" title="w:en:Parity (mathematics)">even</a> <a href="https://en.wikipedia.org/wiki/en:binary" class="extiw" title="w:en:binary">binary</a> <a href="https://en.wikipedia.org/wiki/en:digit_sum" class="extiw" title="w:en:digit sum">digit sums</a> form an <a href="https://en.wikipedia.org/wiki/en:octahedron" class="extiw" title="w:en:octahedron">octahedron</a> and are marked in blue.
<a href="//commons.wikimedia.org/wiki/File:Logical_connectives_Hasse_diagram.svg" class="image"><img alt="Logical connectives Hasse diagram.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/300px-Logical_connectives_Hasse_diagram.svg.png" width="300" height="424" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/450px-Logical_connectives_Hasse_diagram.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/600px-Logical_connectives_Hasse_diagram.svg.png 2x" data-file-width="744" data-file-height="1052"></a>
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
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| current | 01:10, 8 January 2017 | | 360 × 360 (96 KB) | 127.0.0.1 (talk) | The 4D-<a href="https://en.wikipedia.org/wiki/en:hypercube" class="extiw" title="w:en:hypercube">hypercube</a>, layered according to distance from one corner. <br>As described in "Alice in Wonderland" by the <a href="https://en.wikipedia.org/wiki/en:Cheshire_Cat" class="extiw" title="w:en:Cheshire Cat">Cheshire Cat</a>, this vertex-first-shadow of the <a href="https://en.wikipedia.org/wiki/en:tesseract" class="extiw" title="w:en:tesseract">tesseract</a> forms a <a href="https://en.wikipedia.org/wiki/en:rhombic_dodecahedron" class="extiw" title="w:en:rhombic dodecahedron">rhombic dodecahedron</a>.<br><p>Note that the two central (green) vertices should coincide if using an orthogonal projection from 4 to 3 dimensions, but were drawn here slightly apart.<br></p> <p>The eight <a href="https://en.wikipedia.org/wiki/en:nibble" class="extiw" title="w:en:nibble">nibbles</a> with <a href="https://en.wikipedia.org/wiki/en:Parity_(mathematics)" class="extiw" title="w:en:Parity (mathematics)">odd</a> <a href="https://en.wikipedia.org/wiki/en:binary" class="extiw" title="w:en:binary">binary</a> <a href="https://en.wikipedia.org/wiki/en:digit_sum" class="extiw" title="w:en:digit sum">digit sums</a> form a <a href="https://en.wikipedia.org/wiki/en:cube" class="extiw" title="w:en:cube">cube</a> and are marked in white.<br> The two pallindromes 0110 and 1001 (compare <a href="https://en.wikipedia.org/wiki/en:exclusive_or" class="extiw" title="w:en:exclusive or">XOR</a> and <a href="https://en.wikipedia.org/wiki/en:logical_bicontitional" class="extiw" title="w:en:logical bicontitional">XNOR</a>) are projected in the center of the rhombic dodecahedron and are marked in green.<br> The other six nibbles with <a href="https://en.wikipedia.org/wiki/en:Parity_(mathematics)" class="extiw" title="w:en:Parity (mathematics)">even</a> <a href="https://en.wikipedia.org/wiki/en:binary" class="extiw" title="w:en:binary">binary</a> <a href="https://en.wikipedia.org/wiki/en:digit_sum" class="extiw" title="w:en:digit sum">digit sums</a> form an <a href="https://en.wikipedia.org/wiki/en:octahedron" class="extiw" title="w:en:octahedron">octahedron</a> and are marked in blue.<br><a href="//commons.wikimedia.org/wiki/File:Logical_connectives_Hasse_diagram.svg" class="image"><img alt="Logical connectives Hasse diagram.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/300px-Logical_connectives_Hasse_diagram.svg.png" width="300" height="424" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/450px-Logical_connectives_Hasse_diagram.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/600px-Logical_connectives_Hasse_diagram.svg.png 2x" data-file-width="744" data-file-height="1052"></a> </p> <div class="mw-content-ltr"> <table cellspacing="0" style="color:#000;background:#DDD;border:1px solid #BBB;margin:.1em;width:;" class="createdwithtemplate layouttemplate"><tr> <td style="width:1.2em;height:1.2em;padding:.2em;"> <div class="center"><div class="floatnone"><a href="//commons.wikimedia.org/wiki/File:Inkscape_Logo.svg" title="File:Inkscape Logo.svg"><img alt="Inkscape Logo.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Inkscape_Logo.svg/20px-Inkscape_Logo.svg.png" width="20" height="20" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Inkscape_Logo.svg/30px-Inkscape_Logo.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Inkscape_Logo.svg/40px-Inkscape_Logo.svg.png 2x" data-file-width="128" data-file-height="128"></a></div></div> </td> <td style="font-size:.85em;padding:.2em;vertical-align:middle;">This <a href="https://en.wikipedia.org/wiki/Vector_images" class="extiw" title="w:Vector images">vector image</a> was created with <a href="//commons.wikimedia.org/wiki/Help:Inkscape" title="Help:Inkscape">Inkscape</a>. </td> </tr></table> </div> <div class="mw-content-ltr plainlinks"> <table cellspacing="0" style="color:#000;background:#EFE;border:1px solid #55B05A;margin:.1em;width:;"><tr><td style="height:29px;line-height:2.1em;padding:0;vertical-align:middle"> <a href="//validator.w3.org/" rel="nofollow"><img alt="W3C" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Valid_SVG_1.1_%28green%29.svg/88px-Valid_SVG_1.1_%28green%29.svg.png" width="88" height="30" style="vertical-align: top" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Valid_SVG_1.1_%28green%29.svg/132px-Valid_SVG_1.1_%28green%29.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Valid_SVG_1.1_%28green%29.svg/176px-Valid_SVG_1.1_%28green%29.svg.png 2x" data-file-width="91" data-file-height="31"></a><span style="visibility:hidden; 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