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- Truncated_simplectic_honeycomb abstract "In geometry, the truncated simplectic honeycomb (or truncated n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the symmetry of the affine Coxeter group. It is given a Schläfli symbol t{3[n+1]}, and is represented by a Coxeter-Dynkin diagram as a cyclic graph of n+1 nodes with two adjacent nodes ringed. It is composed of n-simplex facets, along with all truncated n-simplices. In n-dimensions, each can be seen as a set of n+1 sets of parallel hyperplanes that divide space. Each hyperplane contains the same honeycomb of one dimension lower.In 1-dimension, the honeycomb represents an apeirogon, with alternately colored line segments. In 2-dimensions, the honeycomb represents the trihexagonal tiling, with Coxeter graph File:CDel branch 11.pngFile:CDel split2.pngFile:CDel node.png. In 3-dimensions it represents the quarter cubic honeycomb, with Coxeter graph File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel branch.png filling space with alternately tetrahedral and truncated tetrahedral cells. In 4-dimensions its called a truncated 5-cell honeycomb, with Coxeter graph File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel split2.pngFile:CDel node.png, with 5-cell, truncated 5-cell, and bitruncated 5-cell facets. In 5-dimensions its called an truncated 5-simplex honeycomb, with Coxeter graph File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel branch.png, filling space by 5-simplex, truncated 5-simplex, and bitruncated 5-simplex facets. In 6-dimensions its called a truncated 6-simplex honeycomb, with Coxeter graph File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel split2.pngFile:CDel node.png, filling space by 6-simplex, truncated 6-simplex, bitruncated 6-simplex, and tritruncated 6-simplex facets.".
- Truncated_simplectic_honeycomb thumbnail Uniform_apeirogon.png?width=300.
- Truncated_simplectic_honeycomb wikiPageExternalLink productCd-0471010030.html.
- Truncated_simplectic_honeycomb wikiPageID "34052377".
- Truncated_simplectic_honeycomb wikiPageRevisionID "572309220".
- Truncated_simplectic_honeycomb hasPhotoCollection Truncated_simplectic_honeycomb.
- Truncated_simplectic_honeycomb subject Category:Honeycombs_(geometry).
- Truncated_simplectic_honeycomb subject Category:Polytopes.
- Truncated_simplectic_honeycomb comment "In geometry, the truncated simplectic honeycomb (or truncated n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the symmetry of the affine Coxeter group. It is given a Schläfli symbol t{3[n+1]}, and is represented by a Coxeter-Dynkin diagram as a cyclic graph of n+1 nodes with two adjacent nodes ringed. It is composed of n-simplex facets, along with all truncated n-simplices.".
- Truncated_simplectic_honeycomb label "Truncated simplectic honeycomb".
- Truncated_simplectic_honeycomb sameAs m.0hr01wr.
- Truncated_simplectic_honeycomb wasDerivedFrom Truncated_simplectic_honeycomb?oldid=572309220.
- Truncated_simplectic_honeycomb depiction Uniform_apeirogon.png.
- Truncated_simplectic_honeycomb isPrimaryTopicOf Truncated_simplectic_honeycomb.
!["In geometry, the truncated simplectic honeycomb (or truncated n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the symmetry of the affine Coxeter group. It is given a Schläfli symbol t{3[n+1]}, and is represented by a Coxeter-Dynkin diagram as a cyclic graph of n+1 nodes with two adjacent nodes ringed. It is composed of n-simplex facets, along with all truncated n-simplices. In n-dimensions, each can be seen as a set of n+1 sets of parallel hyperplanes that divide space. Each hyperplane contains the same honeycomb of one dimension lower.In 1-dimension, the honeycomb represents an apeirogon, with alternately colored line segments. In 2-dimensions, the honeycomb represents the trihexagonal tiling, with Coxeter graph File:CDel branch 11.pngFile:CDel split2.pngFile:CDel node.png. In 3-dimensions it represents the quarter cubic honeycomb, with Coxeter graph File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel branch.png filling space with alternately tetrahedral and truncated tetrahedral cells. In 4-dimensions its called a truncated 5-cell honeycomb, with Coxeter graph File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel split2.pngFile:CDel node.png, with 5-cell, truncated 5-cell, and bitruncated 5-cell facets. In 5-dimensions its called an truncated 5-simplex honeycomb, with Coxeter graph File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel branch.png, filling space by 5-simplex, truncated 5-simplex, and bitruncated 5-simplex facets. In 6-dimensions its called a truncated 6-simplex honeycomb, with Coxeter graph File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel split2.pngFile:CDel node.png, filling space by 6-simplex, truncated 6-simplex, bitruncated 6-simplex, and tritruncated 6-simplex facets."](?object=%22In%20geometry%2C%20the%20truncated%20simplectic%20honeycomb%20(or%20truncated%20n-simplex%20honeycomb)%20is%20a%20dimensional%20infinite%20series%20of%20honeycombs%2C%20based%20on%20the%20symmetry%20of%20the%20affine%20Coxeter%20group.%20It%20is%20given%20a%20Schl%C3%A4fli%20symbol%20t%7B3%5Bn%2B1%5D%7D%2C%20and%20is%20represented%20by%20a%20Coxeter-Dynkin%20diagram%20as%20a%20cyclic%20graph%20of%20n%2B1%20nodes%20with%20two%20adjacent%20nodes%20ringed.%20It%20is%20composed%20of%20n-simplex%20facets%2C%20along%20with%20all%20truncated%20n-simplices.%20In%20n-dimensions%2C%20each%20can%20be%20seen%20as%20a%20set%20of%20n%2B1%20sets%20of%20parallel%20hyperplanes%20that%20divide%20space.%20Each%20hyperplane%20contains%20the%20same%20honeycomb%20of%20one%20dimension%20lower.In%201-dimension%2C%20the%20honeycomb%20represents%20an%20apeirogon%2C%20with%20alternately%20colored%20line%20segments.%20In%202-dimensions%2C%20the%20honeycomb%20represents%20the%20trihexagonal%20tiling%2C%20with%20Coxeter%20graph%20File%3ACDel%20branch%2011.pngFile%3ACDel%20split2.pngFile%3ACDel%20node.png.%20In%203-dimensions%20it%20represents%20the%20quarter%20cubic%20honeycomb%2C%20with%20Coxeter%20graph%20File%3ACDel%20branch%2011.pngFile%3ACDel%203ab.pngFile%3ACDel%20branch.png%20filling%20space%20with%20alternately%20tetrahedral%20and%20truncated%20tetrahedral%20cells.%20In%204-dimensions%20its%20called%20a%20truncated%205-cell%20honeycomb%2C%20with%20Coxeter%20graph%20File%3ACDel%20branch%2011.pngFile%3ACDel%203ab.pngFile%3ACDel%20nodes.pngFile%3ACDel%20split2.pngFile%3ACDel%20node.png%2C%20with%205-cell%2C%20truncated%205-cell%2C%20and%20bitruncated%205-cell%20facets.%20In%205-dimensions%20its%20called%20an%20truncated%205-simplex%20honeycomb%2C%20with%20Coxeter%20graph%20File%3ACDel%20branch%2011.pngFile%3ACDel%203ab.pngFile%3ACDel%20nodes.pngFile%3ACDel%203ab.pngFile%3ACDel%20branch.png%2C%20filling%20space%20by%205-simplex%2C%20truncated%205-simplex%2C%20and%20bitruncated%205-simplex%20facets.%20In%206-dimensions%20its%20called%20a%20truncated%206-simplex%20honeycomb%2C%20with%20Coxeter%20graph%20File%3ACDel%20branch%2011.pngFile%3ACDel%203ab.pngFile%3ACDel%20nodes.pngFile%3ACDel%203ab.pngFile%3ACDel%20nodes.pngFile%3ACDel%20split2.pngFile%3ACDel%20node.png%2C%20filling%20space%20by%206-simplex%2C%20truncated%206-simplex%2C%20bitruncated%206-simplex%2C%20and%20tritruncated%206-simplex%20facets.%22%40en){kind=link}
