en>Andyhowlett: /* Future experiments */

2014-11-06T01:23:08Z

Future experiments

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-!bgcolor=#e7dcc3 colspan=2|quarter cubic honeycomb
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en>BattyBot: fixed CS1 errors: dates & General fixes using AWB (9832)

2014-01-03T01:46:57Z

fixed CS1 errors: dates & General fixes using AWB (9832)

New page

{| class="wikitable" align="right" style="margin-left:10px" width="320"
!bgcolor=#e7dcc3 colspan=2|quarter cubic honeycomb
|-
|bgcolor=#ffffff align=center colspan=2|(No image)
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|bgcolor=#e7dcc3|Type||[[Uniform_polyteron#Regular_and_uniform_honeycombs|Uniform 4-honeycomb]]
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|bgcolor=#e7dcc3|Family||[[Quarter hypercubic honeycomb]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]||t1{4,3,3,4} t1{4,31,1} t3{4,31,1} q{4,3,3,4}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]||
{{CDD|node|4|node_1|3|node|3|node|4|node}} 
{{CDD|node|4|node_1|3|node|split1|nodes}} 
{{CDD|nodes_11|split2|node|3|node|4|node}} 
{{CDD|nodes_10ru|split2|node|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node|3|node|4|node_h1}}
|-
|bgcolor=#e7dcc3|4-face type||[[16-cell|h{4,32}]],[[File:Schlegel_wireframe_16-cell.png|40px]] [[Rectified tesseract|h3{4,32}]], [[File:Schlegel_half-solid_rectified_8-cell.png|40px]]
|-
|bgcolor=#e7dcc3|Cell type||[[tetrahedron|{3,3}]], [[File:Tetrahedron.png|20px]] [[Cuboctahedron|t1{4,3}]], [[File:Cuboctahedron.png|20px]]
|-
|bgcolor=#e7dcc3|Face type||[[Triangle|{3}]] [[Square|{4}]]
|-
|bgcolor=#e7dcc3|[[Edge figure]]||[[File:Square pyramid.png|40px]] [[Square pyramid]]
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|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Rectified_tesseractic_honeycomb_verf.png|80px]] Elongated [[octahedral prism|{3,4}×{}]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]||<math>{\tilde{C}}_4</math> = [4,3,3,4] <math>{\tilde{B}}_4</math> = [4,31,1] <math>{\tilde{D}}_4</math> = [31,1,1,1]
|-
|bgcolor=#e7dcc3|Dual||
|-
|bgcolor=#e7dcc3|Properties||[[vertex-transitive]]
|}
In [[Four-dimensional space|four-dimensional]] [[Euclidean geometry]], the '''rectified tesseractic honeycomb''' is a uniform space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 4-space. It is constructed by a [[rectification (geometry)|rectification]] of a [[tesseractic honeycomb]] which creates new vertices on the middle of all the original edges, rectifying the cells into [[rectified tesseract]]s, and adding new [[16-cell]] facets at the original vertices. Its [[vertex figure]] is an [[octahedral prism]], {3,4}×{}.

It is also called a '''quarter tesseractic honeycomb''' since it has half the vertices of the [[4-demicubic honeycomb]], and a quarter of the vertices of a [[tesseractic honeycomb]].<ref>Coxeter, '''Regular and Semi-Regular Polytopes III''', (1988), p318</ref>


== Related honeycombs==
{{C4_honeycombs}}

{{B4_honeycombs}}

{{D4_honeycombs}}

== See also ==
Regular and uniform honeycombs in 4-space:
*[[Tesseractic honeycomb]]
*[[Demitesseractic honeycomb]]
*[[24-cell honeycomb]]
*[[Truncated 24-cell honeycomb]]
*[[Snub 24-cell honeycomb]]
* [[5-cell honeycomb]]
* [[Truncated 5-cell honeycomb]]
* [[Omnitruncated 5-cell honeycomb]]

==Notes==
{{reflist}}

== References ==
* '''Kaleidoscopes: Selected Writings of H.S.M. Coxeter''', edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45] See p318 [http://books.google.com/books?id=fUm5Mwfx8rAC&lpg=PA318&ots=dnT1LYgmij&dq=%22quarter%20cubic%20honeycomb%22%20q%7B4%2C3%2C4%7D&pg=PA318#v=onepage&q=%22quarter%20cubic%20honeycomb%22%20q%7B4,3,4%7D&f=false]
* [[George Olshevsky]], ''Uniform Panoploid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)''
* {{KlitzingPolytopes|flat.htm|4D|Euclidean tesselations#4D}} o4x3o3o4o, o3o3o *b3x4o, x3o3x *b3o4o, x3o3x *b3o *b3o - rittit - O87
* {{cite book |author=Conway JH, Sloane NJH |year=1998 |title=Sphere Packings, Lattices and Groups |edition=3rd |isbn=0-387-98585-9}}
{{Honeycombs}}

{{DEFAULTSORT:Demitesseractic Honeycomb}}
[[Category:Honeycombs (geometry)]]
[[Category:5-polytopes]]

Warp-field experiments - Revision history

en>Andyhowlett: /* Future experiments */

en>BattyBot: fixed CS1 errors: dates & General fixes using AWB (9832)