Quarter hypercubic honeycomb

In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, the quarter hypercubic honeycomb (or quarter n-cubic honeycomb) is a dimensional infinite series of <a href="/facts/Honeycomb_(geometry)/seyRBcel">honeycombs</a>, based on the <a href="/facts/Hypercube_honeycomb/MQxLbDeB">hypercube honeycomb</a>. It is given a <a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a> q{4,3...3,4} or Coxeter symbol qδ4 representing the regular form with three quarters of the vertices removed and containing the symmetry of <a href="/facts/Coxeter_diagram/Ik6LmXJB">Coxeter group</a> 
 
 
 
 
 
 
 
 D
 ~
 
 
 
 
 n
 −
 1
 
 
 
 
 {\displaystyle {\tilde {D}}_{n-1}}
 
 for n ≥ 5, with 
 
 
 
 
 
 
 
 D
 ~
 
 
 
 
 4
 
 
 
 
 {\displaystyle {\tilde {D}}_{4}}
 
 = 
 
 
 
 
 
 
 
 A
 ~
 
 
 
 
 4
 
 
 
 
 {\displaystyle {\tilde {A}}_{4}}
 
 and for quarter n-cubic honeycombs 
 
 
 
 
 
 
 
 D
 ~
 
 
 
 
 5
 
 
 
 
 {\displaystyle {\tilde {D}}_{5}}
 
 = 
 
 
 
 
 
 
 
 B
 ~
 
 
 
 
 5
 
 
 
 
 {\displaystyle {\tilde {B}}_{5}}
 
.

<table><tbody><tr><th>qδn</th><th>Name</th><th><a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläflisymbol</a></th><th><a href="/facts/Coxeter_diagram/Ik6LmXJB">Coxeter diagrams</a></th><th colspan="3">Facets</th><th><a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a></th></tr><tr><td>qδ3</td><td>quarter <a href="/facts/Square_tiling/3ym86mvv">square tiling</a></td><td>q{4,4}</td><td> or or </td><td>h{4}={2}</td><td>{ }×{ }</td><td></td><td>{ }×{ }</td></tr><tr><td>qδ4</td><td><a href="/facts/Quarter_cubic_honeycomb/22qQazbw">quarter cubic honeycomb</a></td><td>q{4,3,4}</td><td> or or </td><td><a href="/facts/Tetrahedron/7mkSrl6j">h{4,3}</a></td><td><a href="/facts/Truncated_tetrahedron/K9ItvmUK">h2{4,3}</a></td><td></td><td>Elongated<a href="/facts/Triangular_antiprism/G38q92xW">triangular antiprism</a></td></tr><tr><td>qδ5</td><td><a href="/facts/Quarter_tesseractic_honeycomb/P266Jc7y">quarter tesseractic honeycomb</a></td><td>q{4,32,4}</td><td> or or </td><td><a href="/facts/16-cell/X0YAfobw">h{4,32}</a></td><td><a href="/facts/Rectified_tesseract/xfSdmduC">h3{4,32}</a></td><td></td><td><a href="/facts/Octahedral_prism/8UVHkxvl">{3,4}×{}</a></td></tr><tr><td>qδ6</td><td><a href="/facts/Quarter_5-cubic_honeycomb/r3AAQHbg">quarter 5-cubic honeycomb</a></td><td>q{4,33,4}</td><td></td><td><a href="/facts/5-demicube/zvCeNbU2">h{4,33}</a></td><td><a href="/facts/Runcinated_5-demicube/LlxgkUSu">h4{4,33}</a></td><td></td><td><a href="/facts/Rectified_5-cell/2UAMuo2P">Rectified 5-cell</a> antiprism</td></tr><tr><td>qδ7</td><td><a href="/facts/Quarter_6-cubic_honeycomb/vDRQk9kS">quarter 6-cubic honeycomb</a></td><td>q{4,34,4}</td><td></td><td><a href="/facts/6-demicube/1oTufnFp">h{4,34}</a></td><td><a href="/facts/Stericated_6-demicube/CtKV1Wbj">h5{4,34}</a></td><td>{3,3}×{3,3}</td></tr><tr><td>qδ8</td><td><a href="/facts/Quarter_7-cubic_honeycomb/GjVHMBLq">quarter 7-cubic honeycomb</a></td><td>q{4,35,4}</td><td></td><td><a href="/facts/7-demicube/fGVUTvTI">h{4,35}</a></td><td><a href="/facts/Pentellated_7-demicube/cFaI6V34">h6{4,35}</a></td><td>{3,3}×{3,31,1}</td></tr><tr><td>qδ9</td><td><a href="/facts/Quarter_8-cubic_honeycomb/k820gwj2">quarter 8-cubic honeycomb</a></td><td>q{4,36,4}</td><td></td><td><a href="/facts/8-demicube/sWAomIhw">h{4,36}</a></td><td>h7{4,36}</td><td>{3,3}×{3,32,1}{3,31,1}×{3,31,1}</td></tr><tr><td colspan="7"> </td></tr><tr><td>qδn</td><td>quarter n-cubic honeycomb</td><td>q{4,3n−3,4}</td><td>...</td><td>h{4,3n−2}</td><td>hn−2{4,3n−2}</td><td>...</td></tr></tbody></table>

Quarter hypercubic honeycomb open-in-new

Quarter hypercubic honeycomb