Arnold–Givental conjecture: Difference between revisions

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!bgcolor=#e7dcc3 colspan=2|Truncated 16-cell honeycomb
|-
|bgcolor=#ffffff align=center colspan=2|(No image)
|-
|bgcolor=#e7dcc3|Type||Uniform honeycomb
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]||t{3,3,4,3}<BR>h<sub>2</sub>{4,3,3,4}<BR>t{3,3<sup>1,1,1</sup>}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]||{{CDD|node_1|3|node_1|3|node|4|node|3|node}}<BR>{{CDD|nodes_10ru|split2|node_1|3|node|4|node}} = {{CDD|node_h1|4|node|3|node_1|3|node|4|node}}<BR>{{CDD|node_1|3|node_1|splitsplit1|branch3|node}}
|-
|bgcolor=#e7dcc3|4-face type||[[24-cell|{3,4,3}]] [[File:Schlegel wireframe 24-cell.png|40px]]<BR>[[Truncated 16-cell|t{3,3,4}]] [[File:Schlegel half-solid truncated 16-cell.png|40px]]
|-
|bgcolor=#e7dcc3|Cell type||[[Tetrahedron|{3,3}]]<BR>[[Truncated tetrahedron|t{3,3}]]
|-
|bgcolor=#e7dcc3|Face type||[[Triangle|{3}]]<BR>[[Hexagon|{6}]]
|-
|bgcolor=#e7dcc3|[[Vertex figure]]||[[cubic pyramid]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]||<math>{\tilde{F}}_4</math> = [3,3,4,3]<BR><math>{\tilde{B}}_4</math> = [4,3,3<sup>1,1</sup>]<BR><math>{\tilde{D}}_4</math> = [3<sup>1,1,1,1</sup>]
|-
|bgcolor=#e7dcc3|Dual||?
|-
|bgcolor=#e7dcc3|Properties||[[vertex-transitive]]
|}
In [[Four-dimensional space|four-dimensional]] [[Euclidean geometry]], the '''truncated 16-cell honeycomb''' (or '''cantic tesseractic honeycomb''') is a uniform space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 4-space. It is constructed by [[24-cell]] and [[truncated 16-cell]] [[Facet (geometry)|facets]].
 
== Alternate names==
* Truncated hexadecachoric tetracomb / Truncated hexadecachoric honeycomb
 
== Related honeycombs==
{{F4 honeycombs}}
 
{{C4 honeycombs}}
 
{{B4 honeycombs}}
 
{{D4 honeycombs}}
 
== See also ==
Regular and uniform honeycombs in 4-space:
*[[Tesseractic honeycomb]]
* [[16-cell honeycomb]]
*[[24-cell honeycomb]]
*[[Rectified 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]
* [[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}} (x3x3o *b3o4o), (x3x3o *b3o *b3o), x3x3o4o3o - thext - O105
 
{{Honeycombs}}
 
[[Category:Honeycombs (geometry)]]
[[Category:5-polytopes]]

Latest revision as of 22:10, 8 January 2015

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