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Runcinated 5-cubes
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<h2 id="runcinated-5-cube">Runcinated 5-cube</h2> <table><tbody><tr><td colspan="3">Runcinated 5-cube</td></tr><tr><td>Type</td><td colspan="2"><a href="/facts/Uniform_5-polytope/mqxsoqwY">Uniform 5-polytope</a></td></tr><tr><td><a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a></td><td colspan="2">t0,3{4,3,3,3}</td></tr><tr><td><a href="/facts/Coxeter_diagram/Ik6LmXJB">Coxeter diagram</a></td><td colspan="2"></td></tr><tr><td>4-faces</td><td>202</td><td>10 <a href="/facts/Runcinated_tesseract/NqDGHQxp"></a>80 <a href="/facts/3-4_duoprism/jlvkbaXz"></a>80 <a href="/facts/Octahedral_prism/8UVHkxvl"></a>32 <a href="/facts/Rectified_5-cell/2UAMuo2P"></a></td></tr><tr><td>Cells</td><td>1240</td><td>40 <a href="/facts/Cube/65lUaAqN"></a>240 <a href="/facts/Cube/65lUaAqN"></a>320 <a href="/facts/Triangular_prism/Yjp4Kw9M"></a>160 <a href="/facts/Tetrahedron/7mkSrl6j"></a>320 <a href="/facts/Triangular_prism/Yjp4Kw9M"></a>160 <a href="/facts/Octahedron/G38q92xW"></a></td></tr><tr><td>Faces</td><td>2160</td><td>240 <a href="/facts/Square/JHJeMvmL"></a>960 <a href="/facts/Square/JHJeMvmL"></a>640 <a href="/facts/Triangle/cRXUwsMn"></a>320 <a href="/facts/Triangle/cRXUwsMn"></a></td></tr><tr><td>Edges</td><td>1440</td><td>480+960</td></tr><tr><td>Vertices</td><td colspan="2">320</td></tr><tr><td><a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a></td><td colspan="2"></td></tr><tr><td><a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a></td><td colspan="2">B5 [4,3,3,3]</td></tr><tr><td>Properties</td><td colspan="2"><a href="/facts/Convex_polytope/2pRHcRgC">convex</a></td></tr></tbody></table> <h3>Alternate names</h3> <ul><li>Small prismated penteract (Acronym: span) (Jonathan Bowers)</li></ul> <h3>Coordinates</h3> <p>The <a href="/facts/Cartesian_coordinate/lkTqvMmB">Cartesian coordinates</a> of the vertices of a <i>runcinated 5-cube</i> having edge length 2 are all permutations of: </p> ( ± 1 , ± 1 , ± 1 , ± ( 1 + 2 ) , ± ( 1 + 2 ) ) {\displaystyle \left(\pm 1,\ \pm 1,\ \pm 1,\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}})\right)} <h3>Images</h3> <a href="/facts/Orthographic_projection/L3Cv9kYD">orthographic projections</a><table><tbody><tr><th><a href="/facts/Coxeter_plane/4B80wH8V">Coxeter plane</a></th><th>B5</th><th>B4 / D5</th><th>B3 / D4 / A2</th></tr><tr><th>Graph</th><td></td><td></td><td></td></tr><tr><th><a href="/facts/Dihedral_symmetry/1PUlRh4M">Dihedral symmetry</a></th><td>[10]</td><td>[8]</td><td>[6]</td></tr><tr><th>Coxeter plane</th><th>B2</th><th>A3</th></tr><tr><th>Graph</th><td></td><td></td></tr><tr><th>Dihedral symmetry</th><td>[4]</td><td>[4]</td></tr></tbody></table> <h2 id="runcitruncated-5-cube">Runcitruncated 5-cube</h2> <table><tbody><tr><th colspan="3">Runcitruncated 5-cube</th></tr><tr><td>Type</td><td colspan="2"><a href="/facts/Uniform_5-polytope/mqxsoqwY">Uniform 5-polytope</a></td></tr><tr><td><a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a></td><td colspan="2">t0,1,3{4,3,3,3}</td></tr><tr><td><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagrams</a></td><td colspan="2"></td></tr><tr><td>4-faces</td><td>202</td><td>10 <a href="/facts/Runcitruncated_tesseract/NqDGHQxp"></a>80 <a href="/facts/3-8_duoprism/lr0l84cc"></a>80 <a href="/facts/Octahedral_prism/8UVHkxvl"></a>32 <a href="/facts/Cantellated_5-cell/pm158bSU"></a></td></tr><tr><td>Cells</td><td>1560</td><td>40 <a href="/facts/Truncated_cube/XVAUG4fD"></a>240 <a href="/facts/Octagonal_prism/pMnX2f7F"></a>320 <a href="/facts/Triangular_prism/Yjp4Kw9M"></a>320 <a href="/facts/Triangular_prism/Yjp4Kw9M"></a>160 <a href="/facts/Cuboctahedron/hD7p0Mem"></a>320 <a href="/facts/Triangular_prism/Yjp4Kw9M"></a>160 <a href="/facts/Octahedron/G38q92xW"></a></td></tr><tr><td>Faces</td><td>3760</td><td>240 <a href="/facts/Octagon/H5PuP3wP"></a>960 <a href="/facts/Square/JHJeMvmL"></a>320 <a href="/facts/Equilateral_triangle/MJomsYDS"></a>960 <a href="/facts/Square/JHJeMvmL"></a>640 <a href="/facts/Equilateral_triangle/MJomsYDS"></a>640 <a href="/facts/Equilateral_triangle/MJomsYDS"></a></td></tr><tr><td>Edges</td><td>3360</td><td>480+960+1920</td></tr><tr><td>Vertices</td><td colspan="2">960</td></tr><tr><td><a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a></td><td colspan="2"></td></tr><tr><td><a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a></td><td colspan="2">B5, [3,3,3,4]</td></tr><tr><td>Properties</td><td colspan="2"><a href="/facts/Convex_polytope/2pRHcRgC">convex</a></td></tr></tbody></table> <h3>Alternate names</h3> <ul><li>Runcitruncated penteract</li> <li>Prismatotruncated penteract (Acronym: pattin) (Jonathan Bowers)</li></ul> <h3>Construction and coordinates</h3> <p>The <a href="/facts/Cartesian_coordinate/lkTqvMmB">Cartesian coordinates</a> of the vertices of a <i>runcitruncated 5-cube</i> having edge length 2 are all permutations of: </p> ( ± 1 , ± ( 1 + 2 ) , ± ( 1 + 2 ) , ± ( 1 + 2 2 ) , ± ( 1 + 2 2 ) ) {\displaystyle \left(\pm 1,\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+2{\sqrt {2}}),\ \pm (1+2{\sqrt {2}})\right)} <h3>Images</h3> <a href="/facts/Orthographic_projection/L3Cv9kYD">orthographic projections</a><table><tbody><tr><th><a href="/facts/Coxeter_plane/4B80wH8V">Coxeter plane</a></th><th>B5</th><th>B4 / D5</th><th>B3 / D4 / A2</th></tr><tr><th>Graph</th><td></td><td></td><td></td></tr><tr><th><a href="/facts/Dihedral_symmetry/1PUlRh4M">Dihedral symmetry</a></th><td>[10]</td><td>[8]</td><td>[6]</td></tr><tr><th>Coxeter plane</th><th>B2</th><th>A3</th></tr><tr><th>Graph</th><td></td><td></td></tr><tr><th>Dihedral symmetry</th><td>[4]</td><td>[4]</td></tr></tbody></table> <h2 id="runcicantellated-5-cube">Runcicantellated 5-cube</h2> <table><tbody><tr><td colspan="3">Runcicantellated 5-cube</td></tr><tr><td>Type</td><td colspan="2"><a href="/facts/Uniform_5-polytope/mqxsoqwY">Uniform 5-polytope</a></td></tr><tr><td><a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a></td><td colspan="2">t0,2,3{4,3,3,3}</td></tr><tr><td><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></td><td colspan="2"></td></tr><tr><td>4-faces</td><td>202</td><td>10 <a href="/facts/Runcitruncated_16-cell/NqDGHQxp"></a>80 <a href="/facts/3-4_duoprism/jlvkbaXz"></a>80 <a href="/facts/Truncated_tetrahedral_prism/7Fc4E1FP"></a>32 <a href="/facts/Bitruncated_5-cell/oqF6jkb7"></a></td></tr><tr><td>Cells</td><td>1240</td><td>40 <a href="/facts/Rhombicuboctahedron/TmxUmEnl"></a>240 <a href="/facts/Cube/65lUaAqN"></a>320 <a href="/facts/Hexagonal_prism/oxYc0nF2"></a>320 <a href="/facts/Triangular_prism/Yjp4Kw9M"></a>160 <a href="/facts/Truncated_tetrahedron/K9ItvmUK"></a>160 <a href="/facts/Truncated_tetrahedron/K9ItvmUK"></a></td></tr><tr><td>Faces</td><td>2960</td><td>240 <a href="/facts/Square/JHJeMvmL"></a>480 <a href="/facts/Square/JHJeMvmL"></a>960 <a href="/facts/Square/JHJeMvmL"></a>320 <a href="/facts/Equilateral_triangle/MJomsYDS"></a>640 <a href="/facts/Hexagon/DPzuCzWE"></a>320 <a href="/facts/Equilateral_triangle/MJomsYDS"></a></td></tr><tr><td>Edges</td><td>2880</td><td>960+960+960</td></tr><tr><td>Vertices</td><td colspan="2">960</td></tr><tr><td><a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a></td><td colspan="2"></td></tr><tr><td><a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a></td><td colspan="2">B5 [4,3,3,3]</td></tr><tr><td>Properties</td><td colspan="2"><a href="/facts/Convex_polytope/2pRHcRgC">convex</a></td></tr></tbody></table> <h3>Alternate names</h3> <ul><li>Runcicantellated penteract</li> <li>Prismatorhombated penteract (Acronym: prin) (Jonathan Bowers)</li></ul> <h3>Coordinates</h3> <p>The <a href="/facts/Cartesian_coordinate/lkTqvMmB">Cartesian coordinates</a> of the vertices of a <i>runcicantellated 5-cube</i> having edge length 2 are all permutations of: </p> ( ± 1 , ± 1 , ± ( 1 + 2 ) , ± ( 1 + 2 2 ) , ± ( 1 + 2 2 ) ) {\displaystyle \left(\pm 1,\ \pm 1,\ \pm (1+{\sqrt {2}}),\ \pm (1+2{\sqrt {2}}),\ \pm (1+2{\sqrt {2}})\right)} <h3>Images</h3> <a href="/facts/Orthographic_projection/L3Cv9kYD">orthographic projections</a><table><tbody><tr><th><a href="/facts/Coxeter_plane/4B80wH8V">Coxeter plane</a></th><th>B5</th><th>B4 / D5</th><th>B3 / D4 / A2</th></tr><tr><th>Graph</th><td></td><td></td><td></td></tr><tr><th><a href="/facts/Dihedral_symmetry/1PUlRh4M">Dihedral symmetry</a></th><td>[10]</td><td>[8]</td><td>[6]</td></tr><tr><th>Coxeter plane</th><th>B2</th><th>A3</th></tr><tr><th>Graph</th><td></td><td></td></tr><tr><th>Dihedral symmetry</th><td>[4]</td><td>[4]</td></tr></tbody></table> <h2 id="runcicantitruncated-5-cube"> Runcicantitruncated 5-cube</h2> <table><tbody><tr><td colspan="3">Runcicantitruncated 5-cube</td></tr><tr><td>Type</td><td><a href="/facts/Uniform_5-polytope/mqxsoqwY">Uniform 5-polytope</a></td></tr><tr><td><a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a></td><td>t0,1,2,3{4,3,3,3}</td></tr><tr><td><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkindiagram</a></td><td></td></tr><tr><td>4-faces</td><td>202</td></tr><tr><td>Cells</td><td>1560</td></tr><tr><td>Faces</td><td>4240</td></tr><tr><td>Edges</td><td>4800</td></tr><tr><td>Vertices</td><td>1920</td></tr><tr><td><a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a></td><td colspan="2"><a href="/facts/Irregular_5-cell/Rh6lwDcc">Irregular 5-cell</a></td></tr><tr><td><a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a></td><td colspan="2">B5 [4,3,3,3]</td></tr><tr><td>Properties</td><td><a href="/facts/Convex_polytope/2pRHcRgC">convex</a>, <a href="/facts/Isogonal_figure/5nC8PdBm">isogonal</a></td></tr></tbody></table> <h3>Alternate names</h3> <ul><li>Runcicantitruncated penteract</li> <li>Biruncicantitruncated pentacross</li> <li>great prismated penteract (gippin) (Jonathan Bowers)</li></ul> <h3>Coordinates</h3> <p>The <a href="/facts/Cartesian_coordinate/lkTqvMmB">Cartesian coordinates</a> of the vertices of a runcicantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of: </p> ( 1 , 1 + 2 , 1 + 2 2 , 1 + 3 2 , 1 + 3 2 ) {\displaystyle \left(1,\ 1+{\sqrt {2}},\ 1+2{\sqrt {2}},\ 1+3{\sqrt {2}},\ 1+3{\sqrt {2}}\right)} <h3>Images</h3> <a href="/facts/Orthographic_projection/L3Cv9kYD">orthographic projections</a><table><tbody><tr><th><a href="/facts/Coxeter_plane/4B80wH8V">Coxeter plane</a></th><th>B5</th><th>B4 / D5</th><th>B3 / D4 / A2</th></tr><tr><th>Graph</th><td></td><td></td><td></td></tr><tr><th><a href="/facts/Dihedral_symmetry/1PUlRh4M">Dihedral symmetry</a></th><td>[10]</td><td>[8]</td><td>[6]</td></tr><tr><th>Coxeter plane</th><th>B2</th><th>A3</th></tr><tr><th>Graph</th><td></td><td></td></tr><tr><th>Dihedral symmetry</th><td>[4]</td><td>[4]</td></tr></tbody></table> <h2 id="related-polytopes">Related polytopes</h2> <p>These polytopes are a part of a set of 31 <a href="/facts/Uniform_polyteron/mqxsoqwY">uniform polytera</a> generated from the regular <a href="/facts/5-cube/XABdhjof">5-cube</a> or <a href="/facts/5-orthoplex/vU1TvdQ1">5-orthoplex</a>. </p> <table><tbody><tr><th colspan="12">B5 polytopes</th></tr><tr><td><a href="/facts/5-orthoplex/vU1TvdQ1">β5</a></td><td><a href="/facts/Rectified_5-orthoplex/BVp334zE">t1β5</a></td><td><a href="/facts/Birectified_5-cube/81cgLLCG">t2γ5</a></td><td><a href="/facts/Rectified_5-cube/81cgLLCG">t1γ5</a></td><td><a href="/facts/5-cube/XABdhjof">γ5</a></td><td><a href="/facts/Truncated_5-orthoplex/EMvxIKtY">t0,1β5</a></td><td><a href="/facts/Cantellated_5-orthoplex/7bWh33Qz">t0,2β5</a></td><td><a href="/facts/Bitruncated_5-orthoplex/EMvxIKtY">t1,2β5</a></td></tr><tr><td><a href="/facts/Runcinated_5-orthoplex/IcsgoFAF">t0,3β5</a></td><td><a href="/facts/Bicantellated_5-cube/SNt8QftF">t1,3γ5</a></td><td><a href="/facts/Bitruncated_5-cube/kLk4Dwvl">t1,2γ5</a></td><td><a href="/facts/Stericated_5-cube/DCXXtmGr">t0,4γ5</a></td><td><a href="/facts/Runcinated_5-cube/bYexRjL1">t0,3γ5</a></td><td><a href="/facts/Cantellated_5-cube/SNt8QftF">t0,2γ5</a></td><td><a href="/facts/Truncated_5-cube/kLk4Dwvl">t0,1γ5</a></td><td><a href="/facts/Cantitruncated_5-orthoplex/7bWh33Qz">t0,1,2β5</a></td></tr><tr><td><a href="/facts/Runcitruncated_5-orthoplex/IcsgoFAF">t0,1,3β5</a></td><td><a href="/facts/Runcicantellated_5-orthoplex/IcsgoFAF">t0,2,3β5</a></td><td><a href="/facts/Bicantitruncated_5-cube/SNt8QftF">t1,2,3γ5</a></td><td><a href="/facts/Steritruncated_5-orthoplex/DCXXtmGr">t0,1,4β5</a></td><td><a href="/facts/Stericantellated_5-cube/DCXXtmGr">t0,2,4γ5</a></td><td><a href="/facts/Runcicantellated_5-cube/bYexRjL1">t0,2,3γ5</a></td><td><a href="/facts/Steritruncated_5-cube/DCXXtmGr">t0,1,4γ5</a></td><td><a href="/facts/Runcitruncated_5-cube/bYexRjL1">t0,1,3γ5</a></td></tr><tr><td><a href="/facts/Cantitruncated_5-cube/SNt8QftF">t0,1,2γ5</a></td><td><a href="/facts/Runcicantitruncated_5-orthoplex/IcsgoFAF">t0,1,2,3β5</a></td><td><a href="/facts/Stericantitruncated_5-orthoplex/DCXXtmGr">t0,1,2,4β5</a></td><td><a href="/facts/Steriruncitruncated_5-cube/DCXXtmGr">t0,1,3,4γ5</a></td><td><a href="/facts/Stericantitruncated_5-cube/DCXXtmGr">t0,1,2,4γ5</a></td><td><a href="/facts/Runcicantitruncated_5-cube/bYexRjL1">t0,1,2,3γ5</a></td><td><a href="/facts/Omnitruncated_5-cube/DCXXtmGr">t0,1,2,3,4γ5</a></td></tr></tbody></table> <ul><li><a href="/facts/Harold_Scott_MacDonald_Coxeter/D2l5jWGG">H.S.M. Coxeter</a>: <ul><li>H.S.M. Coxeter, <i>Regular Polytopes</i>, 3rd Edition, Dover New York, 1973</li> <li>Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-471-01003-6 <a href="http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html">[1]</a> <ul><li>(Paper 22) H.S.M. Coxeter, <i>Regular and Semi Regular Polytopes I</i>, [Math. Zeit. 46 (1940) 380-407, MR 2,10]</li> <li>(Paper 23) H.S.M. Coxeter, <i>Regular and Semi-Regular Polytopes II</i>, [Math. Zeit. 188 (1985) 559-591]</li> <li>(Paper 24) H.S.M. Coxeter, <i>Regular and Semi-Regular Polytopes III</i>, [Math. Zeit. 200 (1988) 3-45]</li></ul></li></ul></li> <li><a href="/facts/Norman_Johnson_(mathematician)/bQtL9w56">Norman Johnson</a> <i>Uniform Polytopes</i>, Manuscript (1991) <ul><li>N.W. Johnson: <i>The Theory of Uniform Polytopes and Honeycombs</i>, Ph.D.</li></ul></li> <li>Klitzing, Richard. <a href="https://bendwavy.org/klitzing/dimensions/polytera.htm">"5D uniform polytopes (polytera)"</a>. o3x3o3o4x - span, o3x3o3x4x - pattin, o3x3x3o4x - prin, o3x3x3x4x - gippin</li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="https://web.archive.org/web/20070204075028/members.aol.com/Polycell/glossary.html#simplex">Glossary for hyperspace</a>, George Olshevsky.</li> <li><a href="http://www.polytope.net/hedrondude/topes.htm">Polytopes of Various Dimensions</a>, Jonathan Bowers <ul><li><a href="http://www.polytope.net/hedrondude/truncates5.htm">Runcinated uniform polytera</a> (spid), Jonathan Bowers</li></ul></li> <li><a href="http://tetraspace.alkaline.org/glossary.htm">Multi-dimensional Glossary</a></li></ul> <table><tbody><tr><th colspan="13"><ul><li>v</li><li>t</li><li>e</li></ul>Fundamental convex <a href="/facts/Regular_polytope/RYTnEF6Q">regular</a> and <a href="/facts/Uniform_polytope/nFcNAzLy">uniform polytopes</a> in dimensions 2–10</th></tr><tr><th><a href="/facts/Coxeter_group/bgzHFm1Q">Family</a></th><td><a href="/facts/Simple_Lie_group/LkHTNYU9"><i>A</i><i>n</i></a></td><td><a href="/facts/Simple_Lie_group/LkHTNYU9"><i>B</i><i>n</i></a></td><td><i>I</i>2(p) / <a href="/facts/Simple_Lie_group/LkHTNYU9"><i>D</i><i>n</i></a></td><td><a href="/facts/E6_(mathematics)/U9YEMtWj"><i>E</i>6</a> / <a href="/facts/E7_(mathematics)/KjFez9PW"><i>E</i>7</a> / <a href="/facts/E8_(mathematics)/NEaKT71H"><i>E</i>8</a> / <a href="/facts/F4_(mathematics)/30H8CQ8v"><i>F</i>4</a> / <a href="/facts/G2_(mathematics)/Bka4pKjQ"><i>G</i>2</a></td><td><a href="/facts/H4_(mathematics)/bgzHFm1Q">Hn</a></td></tr><tr><th><a href="/facts/Regular_polygon/ws89Nhpt">Regular polygon</a></th><td><a href="/facts/Equilateral_triangle/MJomsYDS">Triangle</a></td><td><a href="/facts/Square/JHJeMvmL">Square</a></td><td><a href="/facts/Regular_polygon/ws89Nhpt">p-gon</a></td><td><a href="/facts/Hexagon/DPzuCzWE">Hexagon</a></td><td><a href="/facts/Pentagon/xoq5oJeQ">Pentagon</a></td></tr><tr><th><a href="/facts/Uniform_polyhedron/PHnprqRC">Uniform polyhedron</a></th><td><a href="/facts/Tetrahedron/7mkSrl6j">Tetrahedron</a></td><td><a href="/facts/Octahedron/G38q92xW">Octahedron</a> • <a href="/facts/Cube/65lUaAqN">Cube</a></td><td><a href="/facts/Tetrahedron/7mkSrl6j">Demicube</a></td><td></td><td><a href="/facts/Regular_dodecahedron/xClYqhcp">Dodecahedron</a> • <a href="/facts/Regular_icosahedron/1U93vmXV">Icosahedron</a></td></tr><tr><th><a href="/facts/Uniform_polychoron/NHxomMxC">Uniform polychoron</a></th><td><a href="/facts/5-cell/Rh6lwDcc">Pentachoron</a></td><td><a href="/facts/16-cell/X0YAfobw">16-cell</a> • <a href="/facts/Tesseract/tlqouBoU">Tesseract</a></td><td><a href="/facts/16-cell/X0YAfobw">Demitesseract</a></td><td><a href="/facts/24-cell/tfoGnlAD">24-cell</a></td><td><a href="/facts/120-cell/W4nroBjJ">120-cell</a> • <a href="/facts/600-cell/tNBtDUe9">600-cell</a></td></tr><tr><th><a href="/facts/Uniform_5-polytope/mqxsoqwY">Uniform 5-polytope</a></th><td><a href="/facts/5-simplex/KIfBFfhl">5-simplex</a></td><td><a href="/facts/5-orthoplex/vU1TvdQ1">5-orthoplex</a> • <a href="/facts/5-cube/XABdhjof">5-cube</a></td><td><a href="/facts/5-demicube/zvCeNbU2">5-demicube</a></td><td></td><td></td></tr><tr><th><a href="/facts/Uniform_6-polytope/pxqFTw2F">Uniform 6-polytope</a></th><td><a href="/facts/6-simplex/mInfSIeH">6-simplex</a></td><td><a href="/facts/6-orthoplex/eGV6o0ol">6-orthoplex</a> • <a href="/facts/6-cube/xN74tdD0">6-cube</a></td><td><a href="/facts/6-demicube/1oTufnFp">6-demicube</a></td><td><a href="/facts/1_22_polytope/7XXjWGQ8">122</a> • <a href="/facts/2_21_polytope/nF3nYaQk">221</a></td><td></td></tr><tr><th><a href="/facts/Uniform_7-polytope/suCJSvTN">Uniform 7-polytope</a></th><td><a href="/facts/7-simplex/6DwtPplH">7-simplex</a></td><td><a href="/facts/7-orthoplex/mIJa3rQp">7-orthoplex</a> • <a href="/facts/7-cube/4af1W7tq">7-cube</a></td><td><a href="/facts/7-demicube/fGVUTvTI">7-demicube</a></td><td><a href="/facts/1_32_polytope/um16Pd2V">132</a> • <a href="/facts/2_31_polytope/zkjkKJ6X">231</a> • <a href="/facts/3_21_polytope/AEUzwA1A">321</a></td><td></td></tr><tr><th><a href="/facts/Uniform_8-polytope/M93v3h3c">Uniform 8-polytope</a></th><td><a href="/facts/8-simplex/QUhcnmk2">8-simplex</a></td><td><a href="/facts/8-orthoplex/dXFkXtPn">8-orthoplex</a> • <a href="/facts/8-cube/vEpKH3le">8-cube</a></td><td><a href="/facts/8-demicube/sWAomIhw">8-demicube</a></td><td><a href="/facts/1_42_polytope/DTgYDddB">142</a> • <a href="/facts/2_41_polytope/R9z0wNUz">241</a> • <a href="/facts/4_21_polytope/QFGglCkk">421</a></td><td></td></tr><tr><th><a href="/facts/Uniform_9-polytope/UdFL9ns2">Uniform 9-polytope</a></th><td><a href="/facts/9-simplex/dHV7qhxN">9-simplex</a></td><td><a href="/facts/9-orthoplex/D7LjUcAh">9-orthoplex</a> • <a href="/facts/9-cube/RNgCPzoM">9-cube</a></td><td><a href="/facts/9-demicube/dkTpfqss">9-demicube</a></td><td></td><td></td></tr><tr><th><a href="/facts/Uniform_10-polytope/Qc5NglV8">Uniform 10-polytope</a></th><td><a href="/facts/10-simplex/oeft7Qjn">10-simplex</a></td><td><a href="/facts/10-orthoplex/x6ysTC9U">10-orthoplex</a> • <a href="/facts/10-cube/mmmyBfJJ">10-cube</a></td><td><a href="/facts/10-demicube/TskxfLy9">10-demicube</a></td><td></td><td></td></tr><tr><th>Uniform <i>n</i>-<a href="/facts/Polytope/a76nXrL0">polytope</a></th><td><i>n</i>-<a href="/facts/Simplex/0FCfNRN8">simplex</a></td><td><i>n</i>-<a href="/facts/Cross-polytope/erk0byF6">orthoplex</a> • <i>n</i>-<a href="/facts/Hypercube/q2mRPbIz">cube</a></td><td><i>n</i>-<a href="/facts/Demihypercube/ackHKsEa">demicube</a></td><td><a href="/facts/Uniform_1_k2_polytope/eqTstjgl">1k2</a> • <a href="/facts/Uniform_2_k1_polytope/pQv1I7AC">2k1</a> • <a href="/facts/Uniform_k_21_polytope/vv3lWMYd">k21</a></td><td><i>n</i>-<a href="/facts/Pentagonal_polytope/4uxePdKt">pentagonal polytope</a></td></tr><tr><th colspan="13">Topics: <a href="/facts/Polytope_families/Gun0RgmR">Polytope families</a> • <a href="/facts/Regular_polytope/RYTnEF6Q">Regular polytope</a> • <a href="/facts/List_of_regular_polytopes_and_compounds/Kng25Ymq">List of regular polytopes and compounds</a></th></tr></tbody></table>