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Bitruncated tesseractic honeycomb
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<table><tbody><tr><th colspan="2">Bitruncated tesseractic honeycomb</th></tr><tr><td colspan="2">(No image)</td></tr><tr><td>Type</td><td><a href="/facts/Uniform_5-polytope/mqxsoqwY">Uniform 4-honeycomb</a></td></tr><tr><td><a href="/facts/Schl%C3%A4fli_symbol/jNQR77UU">Schläfli symbol</a></td><td>t1,2{4,3,3,4} or 2t{4,3,3,4} t1,2{4,31,1} or 2t{4,31,1}t2,3{4,31,1}q2{4,3,3,3,4}</td></tr><tr><td><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></td><td><p> = </p></td></tr><tr><td>4-face type</td><td><a href="/facts/Bitruncated_tesseract/ShQzMKoa">Bitruncated tesseract</a> <a href="/facts/Truncated_16-cell/ShQzMKoa">Truncated 16-cell</a> </td></tr><tr><td>Cell type</td><td><a href="/facts/Octahedron/G38q92xW">Octahedron</a> <a href="/facts/Truncated_tetrahedron/K9ItvmUK">Truncated tetrahedron</a> <a href="/facts/Truncated_octahedron/GA98b4TH">Truncated octahedron</a> </td></tr><tr><td>Face type</td><td>{3}, {4}, {6}</td></tr><tr><td><a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a></td><td><a href="/facts/Square-pyramidal_pyramid/dkCDu1aK">Square-pyramidal pyramid</a></td></tr><tr><td><a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a></td><td> C ~ 4 {\displaystyle {\tilde {C}}_{4}} = [4,3,3,4] B ~ 4 {\displaystyle {\tilde {B}}_{4}} = [4,31,1] D ~ 4 {\displaystyle {\tilde {D}}_{4}} = [31,1,1,1]</td></tr><tr><td>Dual</td><td></td></tr><tr><td>Properties</td><td><a href="/facts/Vertex-transitive/5nC8PdBm">vertex-transitive</a></td></tr></tbody></table> <p>In <a href="/facts/Four-dimensional_space/vFQd0M7T">four-dimensional</a> <a href="/facts/Euclidean_geometry/V6cTcoCy">Euclidean geometry</a>, the bitruncated tesseractic honeycomb is a uniform space-filling <a href="/facts/Tessellation/7BWDywXC">tessellation</a> (or <a href="/facts/Honeycomb_(geometry)/seyRBcel">honeycomb</a>) in Euclidean 4-space. It is constructed by a <a href="/facts/Bitruncation/t0xarbyJ">bitruncation</a> of a <a href="/facts/Tesseractic_honeycomb/fpucRJJn">tesseractic honeycomb</a>. It is also called a cantic quarter tesseractic honeycomb from its q2{4,3,3,4} construction. </p>