Difference between revisions of "Template:A2 honeycombs"

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blackwiki>Tomruen
blackwiki>Cedar101
m (merge <maths>, {{CNone}})
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{| class=wikitable
 
{| class=wikitable
![[Wallpaper group|Wallpaper<BR>group]]
+
! [[Wallpaper group|Wallpaper<BR>group]]
![[:File:Symmetries_of_triangle.png|Triangle<BR>symmetry]]
+
! [[:File:Symmetries_of_triangle.png|Triangle<BR>symmetry]]
![[Coxeter_notation#Extended_symmetry|Extended<BR>symmetry]]
+
! [[Coxeter_notation#Extended_symmetry|Extended<BR>symmetry]]
!Extended<BR>diagram
+
! Extended<BR>diagram
!Extended<BR>group
+
! Extended<BR>group
!Honeycombs
+
! Honeycombs
 
|- style="text-align:center;"
 
|- style="text-align:center;"
!p3m1 (*333)
+
| p3m1 (*333)
!a1 [[File:Triangle_symmetry1.png|40px]]
+
| a1 [[File:Triangle_symmetry1.png|40px]]
![3<sup>[3]</sup>]
+
| [3<sup>[3]</sup>]
!{{CDD|node|split1|branch}}
+
| {{CDD|node|split1|branch}}
|<math>{\tilde{A}}_2</math>
+
| <math>{\tilde{A}}_2</math>
| (none)
+
| {{CNone|(none)}}
 
|- style="text-align:center;"
 
|- style="text-align:center;"
!p6m (*632)
+
| p6m (*632)
!i2 [[File:Triangle_symmetry3.png|40px]]
+
| i2 [[File:Triangle_symmetry3.png|40px]]
!{{Brackets|3<sup>[3]</sup>}} ↔ [6,3]
+
| {{Brackets|3<sup>[3]</sup>}} ↔ [6,3]
!{{CDD|node_c1|split1|branch_c2}} ↔ {{CDD|node_c1|3|node_c2|6|node}}
+
| {{CDD|node_c1|split1|branch_c2}} ↔ {{CDD|node_c1|3|node_c2|6|node}}
| <math>{\tilde{A}}_2</math>×2 ↔ <math>{\tilde{G}}_2</math>
+
| <math>{\tilde{A}}_2 \times 2 \leftrightarrow {\tilde{G}}_2</math>
|{{CDD|node_1|split1|branch}} <sub>[[Triangular tiling|1]]</sub>, {{CDD|node|split1|branch_11}} <sub>[[Trihexagonal tiling|2]]</sub>
+
| {{CDD|node_1|split1|branch}} <sub>[[Triangular tiling|1]]</sub>, {{CDD|node|split1|branch_11}} <sub>[[Trihexagonal tiling|2]]</sub>
 
 
 
|- style="text-align:center;"
 
|- style="text-align:center;"
!p31m (3*3)
+
| p31m (3*3)
!g3 [[File:Triangle_symmetry2.png|40px]]
+
| g3 [[File:Triangle_symmetry2.png|40px]]
![3<sup>+</sup>[3<sup>[3]</sup>]] ↔ [6,3<sup>+</sup>]
+
| [3<sup>+</sup>[3<sup>[3]</sup>]] ↔ [6,3<sup>+</sup>]
!
+
|
|<math>{\tilde{A}}_2</math>×3 ↔ ½ <math>{\tilde{G}}_2</math>
+
| <math>{\tilde{A}}_2 \times 3 \leftrightarrow \tfrac 1 2 {\tilde{G}}_2</math>
|(none)
+
| {{CNone|(none)}}
 
 
 
|- style="text-align:center;"
 
|- style="text-align:center;"
!p6 (632)
+
| p6 (632)
!rowspan=2|r6 [[File:Triangle_symmetry4.png|40px]]
+
|rowspan=2| r6 [[File:Triangle_symmetry4.png|40px]]
![3[3<sup>[3]</sup>]]<sup>+</sup> ↔ [6,3]<sup>+</sup>
+
| [3[3<sup>[3]</sup>]]<sup>+</sup> ↔ [6,3]<sup>+</sup>
!rowspan=2|{{CDD|node_c1|split1|branch_c1}} ↔ {{CDD|node_c1|6|node|3|node}}
+
|rowspan=2| {{CDD|node_c1|split1|branch_c1}} ↔ {{CDD|node_c1|6|node|3|node}}
|½<math>{\tilde{A}}_2</math>×6 ↔ ½ <math>{\tilde{G}}_2</math>
+
| <math>\tfrac 1 2 {\tilde{A}}_2 \times 6 \leftrightarrow \tfrac 1 2 {\tilde{G}}_2</math>
|{{CDD|node_h|split1|branch_hh}} <sub>[[Triangular tiling|(1)]]</sub>
+
| {{CDD|node_h|split1|branch_hh}} <sub>[[Triangular tiling|(1)]]</sub>
 
 
 
|- style="text-align:center;"
 
|- style="text-align:center;"
!p6m (*632)
+
| p6m (*632)
![3[3<sup>[3]</sup>]] ↔ [6,3]
+
| [3[3<sup>[3]</sup>]] ↔ [6,3]
| <math>{\tilde{A}}_2</math>×6 ↔ <math>{\tilde{G}}_2</math>
+
| <math>{\tilde{A}}_2 \times 6 \leftrightarrow {\tilde{G}}_2</math>
|{{CDD|node_1|split1|branch_11}} <sub>[[Hexagonal tiling|3]]</sub>
+
| {{CDD|node_1|split1|branch_11}} <sub>[[Hexagonal tiling|3]]</sub>
 
 
 
|}<noinclude>
 
|}<noinclude>
 
[[Category:Encyclopedic content templates]]
 
[[Category:Encyclopedic content templates]]
 
[[Category:Euclidean_tilings]]
 
[[Category:Euclidean_tilings]]
 
</noinclude>
 
</noinclude>

Revision as of 03:50, 14 July 2018

Wallpaper
group
Triangle
symmetry
Extended
symmetry
Extended
diagram
Extended
group
Honeycombs
p3m1 (*333) a1 40px [3[3]] File:CDel node.pngFile:CDel split1.pngFile:CDel branch.png <math>{\tilde{A}}_2</math> (none)
p6m (*632) i2 40px [[3[3]]] ↔ [6,3] File:CDel node c1.pngFile:CDel split1.pngFile:CDel branch c2.pngFile:CDel node c1.pngFile:CDel 3.pngFile:CDel node c2.pngFile:CDel 6.pngFile:CDel node.png <math>{\tilde{A}}_2 \times 2 \leftrightarrow {\tilde{G}}_2</math> File:CDel node 1.pngFile:CDel split1.pngFile:CDel branch.png 1, File:CDel node.pngFile:CDel split1.pngFile:CDel branch 11.png 2
p31m (3*3) g3 40px [3+[3[3]]] ↔ [6,3+] <math>{\tilde{A}}_2 \times 3 \leftrightarrow \tfrac 1 2 {\tilde{G}}_2</math> (none)
p6 (632) r6 40px [3[3[3]]]+ ↔ [6,3]+ File:CDel node c1.pngFile:CDel split1.pngFile:CDel branch c1.pngFile:CDel node c1.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png <math>\tfrac 1 2 {\tilde{A}}_2 \times 6 \leftrightarrow \tfrac 1 2 {\tilde{G}}_2</math> File:CDel node h.pngFile:CDel split1.pngFile:CDel branch hh.png (1)
p6m (*632) [3[3[3]]] ↔ [6,3] <math>{\tilde{A}}_2 \times 6 \leftrightarrow {\tilde{G}}_2</math> File:CDel node 1.pngFile:CDel split1.pngFile:CDel branch 11.png 3