9-cube

<table><tbody><tr><th colspan="2">9-cubeEnneract</th></tr><tr><td colspan="2"><a href="/facts/Orthogonal_projection/sElXGkxD">Orthogonal projection</a>inside <a href="/facts/Petrie_polygon/uDmot1hD">Petrie polygon</a>Orange vertices are doubled, yellow have 4, and the green center has 8</td></tr><tr><td>Type</td><td>Regular <a href="/facts/9-polytope/UdFL9ns2">9-polytope</a></td></tr><tr><td>Family</td><td><a href="/facts/Hypercube/q2mRPbIz">hypercube</a></td></tr><tr><td><a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a></td><td>{4,37}</td></tr><tr><td><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></td><td></td></tr><tr><td>8-faces</td><td>18 <a href="/facts/8-cube/vEpKH3le">{4,36}</a></td></tr><tr><td>7-faces</td><td>144 <a href="/facts/7-cube/4af1W7tq">{4,35}</a></td></tr><tr><td>6-faces</td><td>672 <a href="/facts/6-cube/xN74tdD0">{4,34}</a></td></tr><tr><td>5-faces</td><td>2016 <a href="/facts/5-cube/XABdhjof">{4,33}</a></td></tr><tr><td>4-faces</td><td>4032 <a href="/facts/Tesseract/tlqouBoU">{4,3,3}</a></td></tr><tr><td>Cells</td><td>5376 <a href="/facts/Cube/65lUaAqN">{4,3}</a></td></tr><tr><td>Faces</td><td>4608 <a href="/facts/Square_(geometry)/JHJeMvmL">{4}</a></td></tr><tr><td>Edges</td><td>2304</td></tr><tr><td>Vertices</td><td>512</td></tr><tr><td><a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a></td><td><a href="/facts/8-simplex/QUhcnmk2">8-simplex</a> </td></tr><tr><td><a href="/facts/Petrie_polygon/uDmot1hD">Petrie polygon</a></td><td><a href="/facts/Octadecagon/cNMQe3va">octadecagon</a></td></tr><tr><td><a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a></td><td>C9, [37,4]</td></tr><tr><td>Dual</td><td><a href="/facts/9-orthoplex/D7LjUcAh">9-orthoplex</a> </td></tr><tr><td>Properties</td><td><a href="/facts/Convex_polytope/2pRHcRgC">convex</a>, <a href="/facts/Hanner_polytope/muTkDlfA">Hanner polytope</a></td></tr></tbody></table>
<p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a 9-cube is a nine-<a href="/facts/Dimension/0ktmUyac">dimensional</a> <a href="/facts/Hypercube/q2mRPbIz">hypercube</a> with 512 <a href="/facts/Vertex_(geometry)/ID3cea9z">vertices</a>, 2304 <a href="/facts/Edge_(geometry)/3lFN6sEz">edges</a>,  4608 <a href="/facts/Square/JHJeMvmL">square</a> <a href="/facts/Face_(geometry)/T2E6BTU4">faces</a>, 5376 <a href="/facts/Cube/65lUaAqN">cubic</a> <a href="/facts/Cell_(mathematics)/T2E6BTU4">cells</a>, 4032 <a href="/facts/Tesseract/tlqouBoU">tesseract</a> <a href="/facts/4-face/T2E6BTU4">4-faces</a>, 2016 <a href="/facts/5-cube/XABdhjof">5-cube</a> <a href="/facts/5-face/T2E6BTU4">5-faces</a>, 672 <a href="/facts/6-cube/xN74tdD0">6-cube</a> <a href="/facts/6-face/T2E6BTU4">6-faces</a>, 144 <a href="/facts/7-cube/4af1W7tq">7-cube</a> <a href="/facts/7-face/T2E6BTU4">7-faces</a>, and 18 <a href="/facts/8-cube/vEpKH3le">8-cube</a> <a href="/facts/8-face/T2E6BTU4">8-faces</a>.
</p><p>It can be named by its <a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a> {4,37}, being composed of three <a href="/facts/8-cube/vEpKH3le">8-cubes</a> around each 7-face. It is also called an enneract, a <a href="/facts/Portmanteau/d124JEbz">portmanteau</a> of <a href="/facts/Tesseract/tlqouBoU">tesseract</a> (the <i>4-cube</i>) and <i>enne</i> for nine (dimensions) in <a href="/facts/Greek_language/pzDd6eIz">Greek</a>. It can also be called a regular octadeca-9-tope or octadecayotton, as a <a href="/facts/9-polytope/UdFL9ns2">nine-dimensional polytope</a> constructed with 18 regular <a href="/facts/Facet_(geometry)/IreRHGJ7">facets</a>.
</p><p>It is a part of an infinite family of polytopes, called hypercubes. The <a href="/facts/Dual_polytope/rkIHbmAf">dual</a> of a 9-cube can be called a <a href="/facts/9-orthoplex/D7LjUcAh">9-orthoplex</a>, and is a part of the infinite family of <a href="/facts/Cross-polytope/erk0byF6">cross-polytopes</a>.
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9-cube open-in-new

9-cube