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{| class="wikitable" width=500
{| class="wikitable mw-collapsible mw-collapsed"
! colspan=9| *''n''42 symmetry mutations of quasiregular tilings: (4.''n'')<sup>2</sup> {{navbar|Quasiregular4 table|brackets=y|mini=y|style=float:right;}}
|+ Dimensional family of quasiregular polyhedra and tilings: ''4.n.4.n''
|-
|-
!rowspan=2|Symmetry<BR>*4n2<BR>[n,4]
!rowspan=2|Symmetry<BR>*4''n''2<BR>[n,4]
!colspan=1|[[List_of_spherical_symmetry_groups|Spherical]]
!colspan=1|[[List_of_spherical_symmetry_groups|Spherical]]
![[List_of_planar_symmetry_groups|Euclidean]]
![[List_of_planar_symmetry_groups|Euclidean]]
!colspan=4|Compact hyperbolic
!colspan=4|Compact hyperbolic
!Paracompact
!Paracompact
!Noncompact
|- valign=top
|- style="vertical-align:top;"
!*342<BR>[3,4]
!*342<BR>[3,4]
!*442<BR>[4,4]
!*442<BR>[4,4]
Line 13: Line 14:
!*642<BR>[6,4]
!*642<BR>[6,4]
!*742<BR>[7,4]
!*742<BR>[7,4]
!*842<BR>[8,4]
!*842<BR>[8,4]...
!*&infin;42<BR>[&infin;,4]
!*&infin;42<BR>[&infin;,4]
!&nbsp;<BR>[''n''i,4]
|- align=center
|- style="text-align:center;"
![[Coxeter diagram|Coxeter]]
!Figures
|{{CDD|node|3|node_1|4|node}}
|[[File:Uniform_tiling_432-t1.png|60px]]
|{{CDD|node|4|node_1|4|node}}
|[[File:Uniform tiling 44-t1.png|60px]]
|{{CDD|node|5|node_1|4|node}}
|[[File:H2-5-4-rectified.svg|60px]]
|{{CDD|node|6|node_1|4|node}}
|[[File:H2 tiling 246-2.png|60px]]
|{{CDD|node|7|node_1|4|node}}
|[[File:H2 tiling 247-2.png|60px]]
|{{CDD|node|8|node_1|4|node}}
|[[File:H2 tiling 248-2.png|60px]]
|{{CDD|node|infin|node_1|4|node}}
|[[File:H2 tiling 24i-2.png|60px]]
|- align=center valign=bottom
|
!Quasiregular<BR>figures<BR>[[Vertex configuration|configuration]]
|- style="text-align:center;"
|[[File:Uniform_tiling_432-t1.png|60px]]<BR>[[Cuboctahedron|4.3.4.3]]
![[Vertex configuration|Config.]]
|[[File:Uniform tiling 44-t1.png|60px]]<BR>[[Square tiling|4.4.4.4]]
|[[Cuboctahedron|(4.3)<sup>2</sup>]]
|[[File:Uniform tiling 54-t1.png|60px]]<BR>[[Tetrapentagonal tiling|4.5.4.5]]
|[[Square tiling|(4.4)<sup>2</sup>]]
|[[File:Uniform tiling 64-t1.png|60px]]<BR>[[Tetrahexagonal tiling|4.6.4.6]]
|[[Tetrapentagonal tiling|(4.5)<sup>2</sup>]]
|[[File:Uniform tiling 74-t1.png|60px]]<BR>[[Tetraheptagonal tiling|4.7.4.7]]
|[[Tetrahexagonal tiling|(4.6)<sup>2</sup>]]
|[[File:Uniform tiling 84-t1.png|60px]]<BR>[[Tetraoctagonal tiling|4.8.4.8]]
|[[Tetraheptagonal tiling|(4.7)<sup>2</sup>]]
|[[File:H2 tiling 24i-2.png|60px]]<br>[[Tetrapeirogonal tiling|4.&infin;.4.&infin;]]
|[[Tetraoctagonal tiling|(4.8)<sup>2</sup>]]
|-
|[[Tetrapeirogonal tiling|(4.&infin;)<sup>2</sup>]]
!colspan=8|Dual figures
|(4.''n''i)<sup>2</sup>
|- align=center
|}<noinclude>
![[Coxeter diagram|Coxeter]]
{{documentation|content=
|{{CDD|node|3|node_f1|4|node}}

|{{CDD|node|4|node_f1|4|node}}
==See also==
|{{CDD|node|5|node_f1|4|node}}
{{Tiling templates}}
|{{CDD|node|6|node_f1|4|node}}

|{{CDD|node|7|node_f1|4|node}}
[[Category:Polyhedra and tiling templates]]
|{{CDD|node|8|node_f1|4|node}}

|{{CDD|node|infin|node_f1|4|node}}
}}</noinclude>
|- align=center valign=bottom
!Dual<BR>(rhombic)<BR>figures<BR>[[Face configuration|configuration]]
|[[File:Rhombicdodecahedron.jpg|60px]]<BR>[[Rhombic dodecahedron|V4.3.4.3]]
|[[File:Uniform tiling 44-t0.png|60px]]<BR>[[Square tiling|V4.4.4.4]]
|[[File:Order-5-4 quasiregular rhombic tiling.png|60px]]<BR>V4.5.4.5
|[[File:Ord64_qreg_rhombic_til.png|60px]]<BR>V4.6.4.6
|[[File:Ord74_qreg_rhombic_til.png|60px]]<BR>V4.7.4.7
|[[File:Ord84_qreg_rhombic_til.png|60px]]<BR>V4.8.4.8
|[[File:Ord4infin qreg rhombic til.png|60px]]<BR>V4.&infin;.4.&infin;
|}

Latest revision as of 13:55, 23 May 2024

*n42 symmetry mutations of quasiregular tilings: (4.n)2
Symmetry
*4n2
[n,4]
Spherical Euclidean Compact hyperbolic Paracompact Noncompact
*342
[3,4]
*442
[4,4]
*542
[5,4]
*642
[6,4]
*742
[7,4]
*842
[8,4]...
*∞42
[∞,4]
 
[ni,4]
Figures
Config. (4.3)2 (4.4)2 (4.5)2 (4.6)2 (4.7)2 (4.8)2 (4.∞)2 (4.ni)2