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Order-6-4 triangular honeycomb
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<table><tbody><tr><th colspan="2">Order-6-4 triangular honeycomb</th></tr><tr><td>Type</td><td><a href="/facts/List_of_regular_polytopes/Kng25Ymq">Regular honeycomb</a></td></tr><tr><td><a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbols</a></td><td>{3,6,4}</td></tr><tr><td><a href="/facts/Coxeter_diagram/Ik6LmXJB">Coxeter diagrams</a></td><td> = </td></tr><tr><td>Cells</td><td><a href="/facts/Triangular_tiling/Jx8f8Krh">{3,6}</a> </td></tr><tr><td>Faces</td><td><a href="/facts/Triangle/cRXUwsMn">{3}</a></td></tr><tr><td>Edge figure</td><td><a href="/facts/Square/JHJeMvmL">{4}</a></td></tr><tr><td>Vertex figure</td><td><a href="/facts/Order-4_hexagonal_tiling/KS6qS8IU">{6,4}</a> r{6,6} </td></tr><tr><td>Dual</td><td><a href="/facts/Order-6-3_square_honeycomb/9hsKdU5I">{4,6,3}</a></td></tr><tr><td><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter group</a></td><td>[3,6,4]</td></tr><tr><td>Properties</td><td>Regular</td></tr></tbody></table> <p>In the <a href="/facts/Geometry/wTQf5ffQ">geometry</a> of <a href="/facts/Hyperbolic_space/kI7tnwdk">hyperbolic 3-space</a>, the order-6-4 triangular honeycomb is a regular space-filling <a href="/facts/Tessellation/7BWDywXC">tessellation</a> (or <a href="/facts/Honeycomb_(geometry)/seyRBcel">honeycomb</a>) with <a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a> {3,6,4}. </p>