Template:Hexagonal tiling table
There are eight uniform tilings that can be based from the regular hexagonal tiling (or the dual triangular tiling). Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms, 7 which are topologically distinct. The truncated triangular tiling is topologically identical to the hexagonal tiling.
| Uniform hexagonal/triangular tilings | |||||||||||
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| Symmetry: [6,3], (*632) | [6,3]+ (632) |
[6,3+] (3*3) | |||||||||
| {6,3} | t{6,3} | r{6,3} | t{3,6} | {3,6} | rr{6,3} | tr{6,3} | sr{6,3} | s{3,6} | |||
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| 63 | 3.122 | (3.6)2 | 6.6.6 | 36 | 3.4.6.4 | 4.6.12 | 3.3.3.3.6 | 3.3.3.3.3.3 | |||
| Uniform duals | |||||||||||
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| V63 | V3.122 | V(3.6)2 | V63 | V36 | V3.4.6.4 | V.4.6.12 | V34.6 | V36 | |||
The hexagonal/triangular tilings also exist as uniform Wythoff constructions in a half symmetry form, in the p3m1, [3[3]], (*333) symmetry group:
| Uniform hexagonal/triangular tilings | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry: h[6,3] = [3[3]], (*333) | [3[3]]+, (333) | ||||||||||
| r{3[3]} | t{3[3]} | {3[3]} | h{6,3} = {3[3]} | h2{6,3} = r{3[3]} | s{3[3]} | ||||||
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| 3.6.3.6 | 6.6.6 | 3.3.3.3.3.3 | 3.3.3.3.3.3 | 3.6.3.6 | 3.3.3.3.3.3 | ||||||
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}}