Order-4-3 pentagonal honeycomb

<table><tbody><tr><th colspan="2">Order-4-3 pentagonal 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 symbol</a></td><td>{5,4,3}</td></tr><tr><td><a href="/facts/Coxeter_diagram/Ik6LmXJB">Coxeter diagram</a></td><td></td></tr><tr><td>Cells</td><td><a href="/facts/Order-4_pentagonal_tiling/aHah4SUB">{5,4}</a> </td></tr><tr><td>Faces</td><td><a href="/facts/Pentagon/jeHEARHH">{5}</a></td></tr><tr><td><a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a></td><td><a href="/facts/Cube/65lUaAqN">{4,3}</a></td></tr><tr><td>Dual</td><td><a href="/facts/Order-5_octahedral_honeycomb/axcmB1c7">{3,4,5}</a></td></tr><tr><td><a href="/facts/Coxeter%25E2%2580%2593Dynkin_diagram/Ik6LmXJB">Coxeter group</a></td><td>[5,4,3]</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-4-3 pentagonal honeycomb or 5,4,3 honeycomb is a regular space-filling <a href="/facts/Tessellation/7BWDywXC">tessellation</a> (or <a href="/facts/Honeycomb_(geometry)/seyRBcel">honeycomb</a>). Each infinite cell is an <a href="/facts/Order-4_pentagonal_tiling/aHah4SUB">order-4 pentagonal tiling</a> whose vertices lie on a <a href="/facts/Hypercycle_(geometry)/5w8YYW78">2-hypercycle</a>, each of which has a limiting circle on the ideal sphere.
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Order-4-3 pentagonal honeycomb open-in-new

Order-4-3 pentagonal honeycomb