Template:Quasiregular4 table: Difference between revisions
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! colspan=9| *''n''42 symmetry mutations of quasiregular tilings: (4.''n'')<sup>2</sup> {{navbar|Quasiregular4 table|brackets=y|mini=y|style=float:right;}} |
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|+ Dimensional family of expanded polyhedra and tilings: ''4.n.4.n'' |
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|- |
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!rowspan=2|Symmetry<BR>* |
!rowspan=2|Symmetry<BR>*4''n''2<BR>[n,4] |
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!colspan=1|[[List_of_spherical_symmetry_groups|Spherical]] |
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![[Spherical polyhedron|polyhedra]] |
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!Euclidean |
![[List_of_planar_symmetry_groups|Euclidean]] |
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!colspan= |
!colspan=4|Compact hyperbolic |
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!Paracompact |
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|- valign=top |
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!Noncompact |
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|- style="vertical-align:top;" |
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!*342<BR>[3,4] |
!*342<BR>[3,4] |
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!*442<BR>[4,4] |
!*442<BR>[4,4] |
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!*642<BR>[6,4] |
!*642<BR>[6,4] |
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!*742<BR>[7,4] |
!*742<BR>[7,4] |
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!*842<BR>[8,4] |
!*842<BR>[8,4]... |
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!*∞42<BR>[∞,4] |
!*∞42<BR>[∞,4] |
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! <BR>[''n''i,4] |
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|- align=center valign=bottom |
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| ⚫ | |||
!Quasiregular<BR>figures<BR>[[Vertex configuration|configuration]] |
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!Figures |
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|[[File:Uniform polyhedron-43-t1.png|50px]]<BR>[[Cuboctahedron|4.3.4.3]] |
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|[[File: |
|[[File:Uniform_tiling_432-t1.png|60px]] |
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|[[File:Uniform tiling |
|[[File:Uniform tiling 44-t1.png|60px]] |
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|[[File:H2-5-4-rectified.svg|60px]] |
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|[[File:Uniform tiling 64-t1.png|50px]]<BR>[[Tetrahexagonal tiling|4.6.4.6]] |
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|[[File:H2 tiling 246-2.png|60px]] |
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|[[File:H2 tiling 247-2.png|60px]] |
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|[[File:H2 tiling |
|[[File:H2 tiling 248-2.png|60px]] |
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|[[File:H2 tiling 24i-2.png|60px]] |
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| ⚫ | |||
| ⚫ | |||
![[Coxeter diagram|Coxeter]] |
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| ⚫ | |||
|{{CDD|node|3|node_1|4|node}} |
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![[Vertex configuration|Config.]] |
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|{{CDD|node|4|node_1|4|node}} |
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|[[Cuboctahedron|(4.3)<sup>2</sup>]] |
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|{{CDD|node|5|node_1|4|node}} |
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|[[Square tiling|(4.4)<sup>2</sup>]] |
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|{{CDD|node|6|node_1|4|node}} |
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|[[Tetrapentagonal tiling|(4.5)<sup>2</sup>]] |
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|{{CDD|node|7|node_1|4|node}} |
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|[[Tetrahexagonal tiling|(4.6)<sup>2</sup>]] |
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|{{CDD|node|8|node_1|4|node}} |
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|[[Tetraheptagonal tiling|(4.7)<sup>2</sup>]] |
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|{{CDD|node|infin|node_1|4|node}} |
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|[[Tetraoctagonal tiling|(4.8)<sup>2</sup>]] |
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|- align=center valign=bottom |
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|[[Tetrapeirogonal tiling|(4.∞)<sup>2</sup>]] |
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!Dual<BR>(rhombic)<BR>figures<BR>[[Face configuration|configuration]] |
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|(4.''n''i)<sup>2</sup> |
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|[[File:Rhombicdodecahedron.jpg|45px]]<BR>[[Rhombic dodecahedron|V4.3.4.3]] |
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|}<noinclude> |
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|[[File:Uniform tiling 44-t0.png|45px]]<BR>[[Square tiling|V4.4.4.4]] |
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{{documentation|content= |
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|V4.5.4.5 |
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|V4.6.4.6 |
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==See also== |
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|V4.7.4.7 |
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{{Tiling templates}} |
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|V4.8.4.8 |
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|V4.∞.4.∞ |
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[[Category:Polyhedra and tiling templates]] |
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| ⚫ | |||
![[Coxeter diagram|Coxeter]] |
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}}</noinclude> |
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|{{CDD|node|3|node_f1|4|node}} |
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|{{CDD|node|4|node_f1|4|node}} |
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|{{CDD|node|5|node_f1|4|node}} |
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|{{CDD|node|6|node_f1|4|node}} |
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|{{CDD|node|7|node_f1|4|node}} |
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|{{CDD|node|8|node_f1|4|node}} |
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|{{CDD|node|infin|node_f1|4|node}} |
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| ⚫ | |||
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 | 
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| Config. | (4.3)2 | (4.4)2 | (4.5)2 | (4.6)2 | (4.7)2 | (4.8)2 | (4.∞)2 | (4.ni)2 |
Template documentationSee also
Tiling templates:
- {{Coxeter–Dynkin diagram}}
- {{Tessellation}}
Tables:
- {{Expanded table}}
- {{Expanded4 table}}
- {{Finite triangular hyperbolic tilings table}}
- {{Hexagonal regular tilings}}
- {{Hexagonal tiling cell tessellations}}
- {{Hexagonal tiling table}}
- {{Hexagonal tiling vertex figure tessellations}}
- {{Infinite triangular hyperbolic tilings table}}
- {{Octagonal regular tilings}}
- {{Omnitruncated symmetric table}}
- {{Omnitruncated table}}
- {{Omnitruncated4 table}}
- {{Order 3-2-2-2 tiling table}}
- {{Order 3-2-3-2 tiling table}}
- {{Order 4-3-3 tiling table}}
- {{Order 4-4 tiling table}} (square)
- {{Order 4-4-3 tiling table}}
- {{Order 4-4-4 tiling table}}
- {{Order 5-3-3 tiling table}}
- {{Order 5-4 tiling table}}
- {{Order 5-4-3 tiling table}}
- {{Order 5-4-4 tiling table}}
- {{Order 5-5 tiling table}}
- {{Order 6-3-3 tiling table}}
- {{Order 6-4 tiling table}}
- {{Order 6-4-3 tiling table}}
- {{Order 6-4-4 tiling table}}
- {{Order 6-5 tiling table}}
- {{Order 6-6 tiling table}}
- {{Order 7-3 tiling table}}
- {{Order 7-4 tiling table}}
- {{Order 7-7 tiling table}}
- {{Order 8-3 tiling table}} (octagonal)
- {{Order 8-4 tiling table}}
- {{Order 8-6 tiling table}}
- {{Order 8-8 tiling table}}
- {{Order i-3 tiling table}}
- {{Order i-3-3 tiling table}}
- {{Order i-4 tiling table}}
- {{Order i-4-3 tiling table}}
- {{Order i-4-4 tiling table}}
- {{Order i-5 tiling table}}
- {{Order i-i tiling table}}
- {{Order i-i-3 tiling table}}
- {{Order i-i-4 tiling table}}
- {{Order i-i-i tiling table}}
- {{Order-3 tiling table}}
- {{Order-4 regular tilings}}
- {{Order-5 regular tilings}}
- {{Order-6 regular tilings}}
- {{Order-7 regular tilings}}
- {{Order-8 regular tilings}}
- {{Quasiregular3 table}}
- {{Quasiregular4 table}}
- {{Quasiregular5 table}}
- {{Quasiregular6 table}}
- {{Quasiregular7 table}}
- {{Quasiregular8 table}}
- {{Regular hyperbolic tiling table}}
- {{Regular pentagonal tiling table}}
- {{Snub table}}
- {{Snub4 table}}
- {{Square regular tiling table}}
- {{Square tiling tessellations}}
- {{Square tiling vertex figure tessellations}}
- {{Triangular regular tiling}}
- {{Triangular tiling table}}
- {{Triangular tiling vertex figure tessellations}}
- {{Truncated figure1 table}}
- {{Truncated figure2 table}}
- {{Truncated figure3 table}}
- {{Truncated figure4 table}}