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Runcinated tesseractic honeycomb
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<table><tbody><tr><th colspan="2">Runcinated 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%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a></td><td>t0,3{4,3,3,4}t0,3{4,3,31,1}</td></tr><tr><td><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></td><td></td></tr><tr><td>4-face type</td><td><a href="/facts/Runcinated_tesseract/NqDGHQxp">runcinated tesseract</a> <a href="/facts/Tesseract/tlqouBoU">tesseract</a> <a href="/facts/Rectified_tesseract/xfSdmduC">rectified tesseract</a> <a href="/facts/Cuboctahedral_prism/fFab3Nyp">cuboctahedral prism</a> </td></tr><tr><td>Cell type</td><td><a href="/facts/Cuboctahedron/hD7p0Mem">Cuboctahedron</a> <a href="/facts/Tetrahedron/7mkSrl6j">Tetrahedron</a> <a href="/facts/Cube/65lUaAqN">Cube</a> <a href="/facts/Triangular_prism/Yjp4Kw9M">Triangular prism</a> </td></tr><tr><td>Face type</td><td>{3}, {4}</td></tr><tr><td><a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a></td><td>triangular-antipodial antifastigium</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}} = [4,3,31,1]</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 runcinated 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/Runcination_(geometry)/nwUxfUIX">runcination</a> of a <a href="/facts/Tesseractic_honeycomb/fpucRJJn">tesseractic honeycomb</a> creating <a href="/facts/Runcinated_tesseract/NqDGHQxp">runcinated tesseracts</a>, and new <a href="/facts/Tesseract/tlqouBoU">tesseract</a>, <a href="/facts/Rectified_tesseract/xfSdmduC">rectified tesseract</a> and <a href="/facts/Cuboctahedral_prism/fFab3Nyp">cuboctahedral prism</a> facets. </p>