en>BG19bot: WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: ^{6 → ⁶ (4) using AWB (9957)}

2014-03-01T08:53:28Z

WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: 6 → 6 (4) using AWB (9957)

← Older revision		Revision as of 10:53, 1 March 2014
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	~~{\| class="wikitable" align="right" style="margin-left:10px" width="320"~~		Hayden is what's published on my birth certification but I do not like when [https://Www.google.com/search?hl=en&gl=us&tbm=nws&q=individuals&btnI=lucky individuals] use my whole title. As a guy what I definitely like is croquet and I would never give it up. Submitting is how I guidance my loved ones. My dwelling is now in Wyoming and my mothers and fathers stay nearby. See what is new on my web page right here: http://www.eurotugowners.com/dB_exp/eta/myd/frm/Salomons-Schoenen.cfm<br><br>Feel free to surf to my webpage :: [http://www.eurotugowners.com/dB_exp/eta/myd/frm/Salomons-Schoenen.cfm Salomons Schoenen]
	~~!bgcolor=#e7dcc3 colspan=2\|quarter 5-cubic honeycomb~~
	\|-
	~~\|bgcolor=#ffffff align=center colspan=2\|(No image)~~
	\|-
	~~\|bgcolor=#e7dcc3\|Type\|\|[[Uniform_polypeton#Regular_and_uniform_honeycombs\|Uniform 5-honeycomb]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|Family\|\|[[Quarter hypercubic honeycomb]]~~
	\|-
	~~\|bgcolor=#e7dcc3\|[~~[~~Schläfli symbol]]\|\|q{4,3,3,3,4}~~
	\|-
	~~\|bgcolor=#e7dcc3\|[[Coxeter-Dynkin diagram]]\|\|{{CDD\|nodes_10ru\|split2\|node\|3\|node\|split1\|nodes_10lu}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node\|3\|node\|4\|node_h1}}~~
	\|-
	~~\|bgcolor=#e7dcc3\|5-face type\|\|[[5-demicube\|h{4,3<sup>3</sup>}]], [[File~~:~~Demipenteract graph ortho.svg\|60px]]<BR>[[Runcinated 5-demicube\|h<sub>4<~~/~~sub>{4,3<sup>3<~~/~~sup>}]], [[File:5-demicube t03 D5~~.~~svg\|60px]]~~
	\|-
	~~\|bgcolor~~=~~#e7dcc3\|[[Vertex figure]]\|\|[[File:Quarter_5-cubic_honeycomb_verf.png\|60px]]<BR>Rectified 5-cell antiprism<BR>or Stretched [[birectified 5-simplex]]~~
	\|-
	~~\|bgcolor~~=~~#e7dcc3\|[[Coxeter group]]\|\|<math>{\tilde{D}}_5</math>×2~~ = ~~[<span/>[3<sup>1,1</sup>,3,3<sup>1,1</sup>]]~~
	\|-
	~~\|bgcolor~~=~~#e7dcc3\|Dual\|\|~~
	\|-
	~~\|bgcolor~~=~~#e7dcc3\|Properties\|\|[[vertex-transitive~~]]
	\|}
	~~In [[Five-dimensional space\|five-dimensional]] [[Euclidean geometry]], the '''quarter 5-cubic honeycomb'''~~ is ~~a uniform space-filling [[tessellation]] (or [[honeycomb (geometry)\|honeycomb]])~~. ~~It has half the vertices of the [[5-demicubic honeycomb]], and a quarter of the vertices of a [[5-cube honeycomb]]~~.~~<ref>Coxeter, '''Regular~~ and ~~Semi-Regular Polytopes III''', (1988), p318</ref> Its facets are [[5-demicube]]s~~ and ~~[[runcinated 5-demicube]]s.~~
	~~<!--==Coordinates==~~

	~~Vertices can be placed at all [[integer]] coordinates (i,j,k,l,m), such that (i+j+k+l+m) [[modulo]] 4=0~~.~~-->~~

	~~== Related honeycombs==~~
	~~{{D5 honeycombs}}~~
	== See ~~also ==~~
	~~Regular and uniform honeycombs in 5-space:~~
	*[[5-cube honeycomb]]
	*[[5-demicube honeycomb]]
	* [[5-simplex honeycomb]]
	* [[Truncated 5-simplex honeycomb]]
	* [[Omnitruncated 5-simplex 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]~~
	* {{KlitzingPolytopes\|flat.~~htm\|5D\|Euclidean tesselations#5D}} x3o3o x3o3o b3e - spaquinoh~~
	~~{{Honeycombs}}~~

	~~[[Category:Honeycombs (geometry)]]~~
	~~[[Category:6-polytopes]~~]

en>Tomruen: /* See also */

2013-08-22T03:13:41Z

See also

New page

{| class="wikitable" align="right" style="margin-left:10px" width="320"
!bgcolor=#e7dcc3 colspan=2|quarter 5-cubic honeycomb
|-
|bgcolor=#ffffff align=center colspan=2|(No image)
|-
|bgcolor=#e7dcc3|Type||[[Uniform_polypeton#Regular_and_uniform_honeycombs|Uniform 5-honeycomb]]
|-
|bgcolor=#e7dcc3|Family||[[Quarter hypercubic honeycomb]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]||q{4,3,3,3,4}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]||{{CDD|nodes_10ru|split2|node|3|node|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node|3|node|3|node|4|node_h1}}
|-
|bgcolor=#e7dcc3|5-face type||[[5-demicube|h{4,33}]], [[File:Demipenteract graph ortho.svg|60px]] [[Runcinated 5-demicube|h4{4,33}]], [[File:5-demicube t03 D5.svg|60px]]
|-
|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Quarter_5-cubic_honeycomb_verf.png|60px]] Rectified 5-cell antiprism or Stretched [[birectified 5-simplex]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]||<math>{\tilde{D}}_5</math>×2 = [[31,1,3,31,1]]
|-
|bgcolor=#e7dcc3|Dual||
|-
|bgcolor=#e7dcc3|Properties||[[vertex-transitive]]
|}
In [[Five-dimensional space|five-dimensional]] [[Euclidean geometry]], the '''quarter 5-cubic honeycomb''' is a uniform space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). It has half the vertices of the [[5-demicubic honeycomb]], and a quarter of the vertices of a [[5-cube honeycomb]].<ref>Coxeter, '''Regular and Semi-Regular Polytopes III''', (1988), p318</ref> Its facets are [[5-demicube]]s and [[runcinated 5-demicube]]s.


== Related honeycombs==
{{D5 honeycombs}}
== See also ==
Regular and uniform honeycombs in 5-space:
*[[5-cube honeycomb]]
*[[5-demicube honeycomb]]
* [[5-simplex honeycomb]]
* [[Truncated 5-simplex honeycomb]]
* [[Omnitruncated 5-simplex 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]
* {{KlitzingPolytopes|flat.htm|5D|Euclidean tesselations#5D}} x3o3o x3o3o *b3*e - spaquinoh
{{Honeycombs}}

[[Category:Honeycombs (geometry)]]
[[Category:6-polytopes]]

Truncated 7-simplex honeycomb - Revision history

en>BG19bot: WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: 6 → 6 (4) using AWB (9957)

en>Tomruen: /* See also */

en>BG19bot: WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: ^{6 → ⁶ (4) using AWB (9957)}