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Template:B4 honeycombs

The [4,3,31,1], {{CDD|node|4|node|3|node|split1|nodes}}, 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.

class="wikitable mw-collapsible mw-collapsed"

!colspan=5| B4 honeycombs

Extended
symmetry

!Extended
diagram

!Order

!Honeycombs

style="text-align:center;"

![4,3,31,1]:

!{{CDD|node_c5|4|node_c4|3|node_c3|split1|nodeab_c1-2}}

!×1

|

{{CDD|node_1|4|node|3|node|split1|nodes_10lu}} 5,

{{CDD|node_1|4|node_1|3|node|split1|nodes_10lu}} 6,

{{CDD|node_1|4|node|3|node_1|split1|nodes_10lu}} 7,

{{CDD|node_1|4|node_1|3|node_1|split1|nodes_10lu}} 8

style="text-align:center;"

!<[4,3,31,1]>:
↔[4,3,3,4]

!{{CDD|node_c5|4|node_c4|3|node_c3|split1|nodeab_c1}}
↔ {{CDD|node_c5|4|node_c4|3|node_c3|3|node_c1|4|node}}

!×2

|

{{CDD|node_1|4|node|3|node|split1|nodes}} 9,

{{CDD|node|4|node_1|3|node|split1|nodes}} 10,

{{CDD|node_1|4|node_1|3|node|split1|nodes}} 11,

{{CDD|node_1|4|node|3|node_1|split1|nodes}} 12,

{{CDD|node|4|node_1|3|node_1|split1|nodes}} 13,

{{CDD|node_1|4|node_1|3|node_1|split1|nodes}} 14,

{{CDD|node|4|node|3|node|split1|nodes_11}} (10),

{{CDD|node_1|4|node|3|node|split1|nodes_11}} 15,

{{CDD|node_1|4|node_1|3|node|split1|nodes_11}} 16,

{{CDD|node|4|node|3|node_1|split1|nodes_11}} (13),

{{CDD|node_1|4|node|3|node_1|split1|nodes_11}} 17,

{{CDD|node_1|4|node_1|3|node_1|split1|nodes_11}} 18,

{{CDD|node_h1|4|node|3|node|split1|nodes}} 19

style="text-align:center;"

![3[1+,4,3,31,1]]
↔ [3[3,31,1,1]]
↔ [3,3,4,3]

!{{CDD|node_c3|3|node_c2|split1|nodeab_c1|4a|nodea}}
↔ {{CDD|node_c3|3|node_c2|splitsplit1|branch3_c1|node_c1}}
↔ {{CDD|node_c3|3|node_c2|3|node_c1|4|node|3|node}}

!×3

|

{{CDD|node|4|node|3|node|split1|nodes_10lu}} 1,

{{CDD|node|4|node|3|node_1|split1|nodes_10lu}} 2,

{{CDD|node|4|node_1|3|node|split1|nodes_10lu}} 3,

{{CDD|node|4|node_1|3|node_1|split1|nodes_10lu}} 4

style="text-align:center;"

![(3,3)[1+,4,3,31,1]]
↔ [(3,3)[31,1,1,1]]
↔ [3,4,3,3]

!{{CDD|node|4|node_c1|3|node_c2|split1|nodeab_c1}}
↔ {{CDD|nodeab_c1|split2|node_c2|split1|nodeab_c1}}
↔ {{CDD|node_c2|3|node_c1|4|node|3|node|3|node}}

!×12

|

{{CDD|node|4|node|3|node_1|split1|nodes}} 20,

{{CDD|node|4|node_1|3|node|split1|nodes_11}} 21,

{{CDD|node|4|node_1|3|node_1|split1|nodes_11}} 22,

{{CDD|node|4|node_h|3|node_h|split1|nodes_hh}} 23

References

{{reflist}}

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