Backpressure routing: Difference between revisions

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m Removing "Bp-rate-selection-example.jpg", it has been deleted from Commons by Fastily because: No license since 24 August 2013: you may re-upload, but please include a license tag.
→Choosing the optimal commodity: Changed 'general' to 'extreme' because all nodes within range is not a general case. Extreme describes it better.
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{| class="wikitable" align="right" style="margin-left:10px" width="320"
[http://Mondediplo.com/spip.php?page=recherche&recherche=Sherwood Sherwood] is what you can get in touch with him and his wife won't like it at all. Missouri has often been his residing place and he loves every day residing there. He is definitely fond of to jog but he has not built a dime with it. Program establishing is what he does for a living. Test out his site listed here: http://digi-mori.com/kochi-yamanohi/userinfo.php?uid=258446<br><br>Have a look at my web blog - [http://digi-mori.com/kochi-yamanohi/userinfo.php?uid=258446 ropa interior para hombres]
!bgcolor=#e7dcc3 colspan=2|Truncated 24-cell honeycomb
|-
|bgcolor=#ffffff align=center colspan=2|(No image)
|-
|bgcolor=#e7dcc3|Type||[[Uniform_polyteron#Regular_and_uniform_honeycombs|Uniform 4-honeycomb]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]||t{3,4,3,3}<BR>tr{3,3,4,3}<BR>t2r{4,3,3,4}<BR>t2r{4,3,3<sup>1,1</sup>}<BR>t{3<sup>1,1,1,1</sup>}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]s||
{{CDD|node_1|3|node_1|4|node|3|node|3|node}}<BR>
{{CDD|node_1|3|node_1|3|node_1|4|node|3|node}}<BR>
{{CDD|node|4|node_1|3|node_1|3|node_1|4|node}}<BR>
{{CDD|nodes_11|split2|node_1|3|node_1|4|node}}<BR>
{{CDD|nodes_11|split2|node_1|split1|nodes_11}}
|-
|bgcolor=#e7dcc3|4-face type||[[Tesseract]] [[File:Schlegel wireframe 8-cell.png|40px]]<BR>[[Truncated 24-cell]] [[File:Schlegel half-solid truncated 24-cell.png|40px]]
|-
|bgcolor=#e7dcc3|Cell type||[[Cube]] [[File:Hexahedron.png|20px]]<BR>[[Truncated octahedron]] [[File:Truncated octahedron.png|20px]]
|-
|bgcolor=#e7dcc3|Face type||[[Square (geometry)|Square]]<BR>[[Triangle]]
|-
|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Truncated 24-cell honeycomb verf.png|80px]]<BR>[[Tetrahedral pyramid]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]s||<math>{\tilde{F}}_4</math>, [3,4,3,3]<BR><math>{\tilde{B}}_4</math>, [4,3,3<sup>1,1</sup>]<BR><math>{\tilde{C}}_4</math>, [4,3,3,4]<BR><math>{\tilde{D}}_4</math>, [3<sup>1,1,1,1</sup>]
|-
|bgcolor=#e7dcc3|Properties||[[Vertex transitive]]
|}
In [[Four-dimensional space|four-dimensional]] [[Euclidean geometry]], the '''truncated 24-cell honeycomb''' is a uniform space-filling [[honeycomb (geometry)|honeycomb]]. It can be seen as a [[Truncation (geometry)|truncation]] of the regular [[24-cell honeycomb]], containing [[tesseract]] and [[truncated 24-cell]] cells.  
 
It has a uniform [[Alternation (geometry)|alternation]], called the [[snub 24-cell honeycomb]]. It is a true snub from the <math>{\tilde{D}}_4</math> construction. This truncated 24-cell has [[Schläfli symbol]] t{3<sup>1,1,1,1</sup>}, and its [[Snub (geometry)|snub]] is represented as s{3<sup>1,1,1,1</sup>}.
 
== Alternate names==
* Truncated icositetrachoric tetracomb
* Truncated icositetrachoric honeycomb
* Cantitruncated 16-cell honeycomb
* Bicantitruncated tesseractic honeycomb
 
== Symmetry constructions ==
 
There are five different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored [[truncated 24-cell]] facets. In all cases, four truncated 24-cells, and one [[tesseract]] meet at each vertex, but the vertex figures have different symmetry generators.
 
{|class="wikitable"
![[Coxeter group]]
![[Coxeter-Dynkin diagram|Coxeter<BR>diagram]]
![[Facet (geometry)|Facets]]
![[Vertex figure]]
!Vertex<BR>figure<BR>symmetry<BR>(order)
|- align=center
|<math>{\tilde{F}}_4</math><BR>= [3,4,3,3]
|{{CDD|node_1|3|node_1|4|node|3|node|3|node}}
|'''4:''' {{CDD|node_1|3|node_1|4|node|3|node}}<BR>'''1:''' {{CDD|node_1|4|node|3|node|3|node}}
|[[File:Truncated 24-cell honeycomb verf.png|80px]]
|{{CDD|node|3|node|3|node}}, [3,3]<BR>(24)
|- align=center
|<math>{\tilde{F}}_4</math><BR>= [3,3,4,3]
|{{CDD|node_1|3|node_1|3|node_1|4|node|3|node}}
|'''3:''' {{CDD|node|3|node|4|node_1|3|node_1}}<BR>'''1:''' {{CDD|node|4|node_1|3|node_1|3|node_1}}<BR>'''1:''' {{CDD|node|4|node|3|node_1|2|node_1}}
|[[File:Truncated 24-cell honeycomb F4b verf.png|80px]]
|{{CDD|node|3|node}}, [3]<BR>(6)
|- align=center
|<math>{\tilde{C}}_4</math><BR>= [4,3,3,4]
|{{CDD|node|4|node_1|3|node_1|3|node_1|4|node}}
|'''2,2:''' {{CDD|node_1|3|node_1|3|node_1|4|node}}<BR>'''1:''' {{CDD|node|4|node_1|2|node_1|4|node}}
|[[File:Truncated 24-cell honeycomb C4 verf.png|80px]]
|{{CDD|node|2|node}}, [2]<BR>(4)
|- align=center
|<math>{\tilde{B}}_4</math><BR>= [3<sup>1,1</sup>,3,4]
|{{CDD|nodes_11|split2|node_1|3|node_1|4|node}}
|'''1,1:''' {{CDD|node_1|3|node_1|3|node_1|4|node}}<BR>'''2:''' {{CDD|nodes_11|split2|node_1|3|node_1}}<BR>'''1:''' {{CDD|node_1|2|node_1|2|node_1|4|node}}
|[[File:Truncated 24-cell honeycomb B4 verf.png|80px]]
|{{CDD|node}}, [ ]<BR>(2)
|- align=center
|<math>{\tilde{D}}_4</math><BR>= [3<sup>1,1,1,1</sup>]
|{{CDD|nodes_11|split2|node_1|split1|nodes_11}}
|'''1,1,1,1:'''<BR>{{CDD|nodes_11|split2|node_1|3|node_1}}<BR>'''1:''' {{CDD|node_1|2|node_1|2|node_1|2|node_1}}
|[[File:Truncated 24-cell honeycomb D4 verf.png|80px]]
|[ ]<sup>+</sup><BR>(1)
|}
 
== 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]]
*[[Snub 24-cell honeycomb]]
*[[5-cell honeycomb]]
*[[Truncated 5-cell honeycomb]]
*[[Omnitruncated 5-cell honeycomb]]
 
== References ==
* [[Coxeter|Coxeter, H.S.M.]] ''[[Regular Polytopes (book)|Regular Polytopes]]'', (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p.&nbsp;296, Table II: Regular honeycombs
* '''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)'' Model 99
* {{KlitzingPolytopes|flat.htm|4D|Euclidean tesselations}} o4x3x3x4o, x3x3x *b3x4o, x3x3x *b3x *b3x, o3o3o4x3x, x3x3x4o3o - ticot - O99
{{Honeycombs}}
[[Category:5-polytopes]]
[[Category:Honeycombs (geometry)]]

Revision as of 15:47, 4 March 2014

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