Template:A6 honeycombs

This honeycomb is one of 17 unique uniform honeycombs* {{mathworld | urlname = Necklace | title = Necklace}}, {{OEIS el|1=A000029}} 18-1 cases, skipping one with zero marks constructed by

the ${\tilde{A}}_6$ Coxeter group, grouped by their extended symmetry of the Coxeter–Dynkin diagrams:

class="wikitable mw-collapsible mw-collapsed" !colspan=5\| A6 honeycombs
Heptagon symmetry !Extended symmetry !Extended diagram !Extended group !Honeycombs
style="text-align:center;" !a1 ![3^[7]] \|{{CDD\|node\|split1\|nodes\|3ab\|nodes\|3ab\|branch}} \| ${\tilde{A}}_6$ \| {{CDD\|node_1\|split1\|nodes_10lur\|3ab\|nodes\|3ab\|branch_10l}} {{CDD\|node_1\|split1\|nodes_11\|3ab\|nodes\|3ab\|branch_10l}}
style="text-align:center;" !i2 !{{Brackets\|3^{{{Bracket\|7}}}}} \|{{CDD\|node_c1\|split1\|nodeab_c2\|3ab\|nodeab_c3\|3ab\|branch_c4}} \| ${\tilde{A}}_6$ ×2 \| {{CDD\|node_1\|split1\|nodes\|3ab\|nodes\|3ab\|branch}}₁ {{CDD\|node_1\|split1\|nodes_11\|3ab\|nodes\|3ab\|branch}} {{CDD\|node_1\|split1\|nodes\|3ab\|nodes_11\|3ab\|branch}} {{CDD\|node_1\|split1\|nodes\|3ab\|nodes\|3ab\|branch_11}} {{CDD\|node_1\|split1\|nodes_11\|3ab\|nodes_11\|3ab\|branch}} {{CDD\|node_1\|split1\|nodes_11\|3ab\|nodes\|3ab\|branch_11}} {{CDD\|node_1\|split1\|nodes\|3ab\|nodes_11\|3ab\|branch_11}} {{CDD\|node\|split1\|nodes_11\|3ab\|nodes\|3ab\|branch}} {{CDD\|node\|split1\|nodes\|3ab\|nodes_11\|3ab\|branch}} {{CDD\|node\|split1\|nodes\|3ab\|nodes\|3ab\|branch_11}}₂ {{CDD\|node\|split1\|nodes_11\|3ab\|nodes_11\|3ab\|branch}} {{CDD\|node\|split1\|nodes_11\|3ab\|nodes\|3ab\|branch_11}} {{CDD\|node\|split1\|nodes\|3ab\|nodes_11\|3ab\|branch_11}} {{CDD\|node\|split1\|nodes_11\|3ab\|nodes_11\|3ab\|branch_11}}
style="text-align:center;" !r14 ![7[3^[7]]] \|{{CDD\|node_c1\|split1\|nodeab_c1\|3ab\|nodeab_c1\|3ab\|branch_c1}} \| ${\tilde{A}}_6$ ×14 \| {{CDD\|node_1\|split1\|nodes_11\|3ab\|nodes_11\|3ab\|branch_11}}₃

class="wikitable mw-collapsible mw-collapsed"

!colspan=5| A6 honeycombs

Heptagon
symmetry

!Extended
symmetry

!Extended
diagram

!Extended
group

!Honeycombs

style="text-align:center;"

!a1

![3^[7]]

|{{CDD|node|split1|nodes|3ab|nodes|3ab|branch}}

| ${\tilde{A}}_6$

style="text-align:center;"

!i2

!{{Brackets|3^{{{Bracket|7}}}}}

|{{CDD|node_c1|split1|nodeab_c2|3ab|nodeab_c3|3ab|branch_c4}}

| ${\tilde{A}}_6$ ×2

{{CDD|node_1|split1|nodes|3ab|nodes|3ab|branch}}₁

{{CDD|node|split1|nodes|3ab|nodes|3ab|branch_11}}₂

style="text-align:center;"

!r14

![7[3^[7]]]

|{{CDD|node_c1|split1|nodeab_c1|3ab|nodeab_c1|3ab|branch_c1}}

| ${\tilde{A}}_6$ ×14

{{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|branch_11}}₃

References

Category:Article shared content templates