The [4,3,31,1], File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes.png, Coxeter group generates 31 permutations of uniform tessellations, 23 with distinct symmetry and 4 with distinct geometry. There are two alternated forms: the alternations (19) and (24) have the same geometry as the 16-cell honeycomb and snub 24-cell honeycomb respectively.
| B4 honeycombs
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Extended symmetry
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Extended diagram
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Order
|
Honeycombs
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| [4,3,31,1]:
|
File:CDel node c5.pngFile:CDel 4.pngFile:CDel node c4.pngFile:CDel 3.pngFile:CDel node c3.pngFile:CDel split1.pngFile:CDel nodeab c1-2.png
|
×1
|
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png 5,
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png 6,
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 10lu.png 7,
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 10lu.png 8
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<[4,3,31,1]>: ↔[4,3,3,4]
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File:CDel node c5.pngFile:CDel 4.pngFile:CDel node c4.pngFile:CDel 3.pngFile:CDel node c3.pngFile:CDel split1.pngFile:CDel nodeab c1.png ↔ File:CDel node c5.pngFile:CDel 4.pngFile:CDel node c4.pngFile:CDel 3.pngFile:CDel node c3.pngFile:CDel 3.pngFile:CDel node c1.pngFile:CDel 4.pngFile:CDel node.png
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×2
|
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes.png 9,
File:CDel node.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes.png 10,
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes.png 11,
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.png 12,
File:CDel node.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.png 13,
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.png 14,
File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 11.png (10),
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 11.png 15,
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 11.png 16,
File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 11.png (13),
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 11.png 17,
File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 11.png 18,
File:CDel node h1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes.png 19
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[3[1+,4,3,31,1]] ↔ [3[3,31,1,1]] ↔ [3,3,4,3]
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File:CDel node c3.pngFile:CDel 3.pngFile:CDel node c2.pngFile:CDel split1.pngFile:CDel nodeab c1.pngFile:CDel 4a.pngFile:CDel nodea.png ↔ File:CDel node c3.pngFile:CDel 3.pngFile:CDel node c2.pngFile:CDel splitsplit1.pngFile:CDel branch3 c1.pngFile:CDel node c1.png ↔ File:CDel node c3.pngFile:CDel 3.pngFile:CDel node c2.pngFile:CDel 3.pngFile:CDel node c1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png
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×3
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File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png 1,
File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 10lu.png 2,
File:CDel node.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png 3,
File:CDel node.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 10lu.png 4
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[(3,3)[1+,4,3,31,1]] ↔ [(3,3)[31,1,1,1]] ↔ [3,4,3,3]
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File:CDel node.pngFile:CDel 4.pngFile:CDel node c1.pngFile:CDel 3.pngFile:CDel node c2.pngFile:CDel split1.pngFile:CDel nodeab c1.png ↔ File:CDel nodeab c1.pngFile:CDel split2.pngFile:CDel node c2.pngFile:CDel split1.pngFile:CDel nodeab c1.png ↔ File:CDel node c2.pngFile:CDel 3.pngFile:CDel node c1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png
|
×12
|
File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.png 20,
File:CDel node.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 11.png 21,
File:CDel node.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 11.png 22,
File:CDel node.pngFile:CDel 4.pngFile:CDel node h.pngFile:CDel 3.pngFile:CDel node h.pngFile:CDel split1.pngFile:CDel nodes hh.png 23
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References