Trioctagonal tiling
Jump to navigation
Jump to search
| Trioctagonal tiling | |
|---|---|
| Trioctagonal tiling Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | (3.8)2 |
| Schläfli symbol | r{8,3} or |
| Wythoff symbol | 2 | 8 3| 3 3 | 4 |
| Coxeter diagram | File:CDel node.pngFile:CDel 8.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png or File:CDel node 1.pngFile:CDel split1-83.pngFile:CDel nodes.png File:CDel label4.pngFile:CDel branch 11.pngFile:CDel split2.pngFile:CDel node.png |
| Symmetry group | [8,3], (*832) [(4,3,3)], (*433) |
| Dual | Order-8-3 rhombille tiling |
| Properties | Vertex-transitive edge-transitive |
In geometry, the trioctagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 octagonal tiling. There are two triangles and two octagons alternating on each vertex. It has Schläfli symbol of r{8,3}.
Symmetry
[edit | edit source]| File:H2 tiling 334-3.png The half symmetry [1+,8,3] = [(4,3,3)] can be shown with alternating two colors of triangles, by Coxeter diagram File:CDel label4.pngFile:CDel branch 11.pngFile:CDel split2.pngFile:CDel node.png. |
File:Uniform dual tiling 433-t01.png Dual tiling |
Related polyhedra and tilings
[edit | edit source]From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular octagonal 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.
It can also be generated from the (4 3 3) hyperbolic tilings:
The trioctagonal tiling can be seen in a sequence of quasiregular polyhedrons and tilings:
See also
[edit | edit source]
Wikimedia Commons has media related to Uniform tiling 3-8-3-8.
- Trihexagonal tiling - 3.6.3.6 tiling
- Rhombille tiling - dual V3.6.3.6 tiling
- Tilings of regular polygons
- List of uniform tilings
References
[edit | edit source]- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value). (Chapter 19, The Hyperbolic Archimedean Tessellations)
- Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
External links
[edit | edit source]- Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- Hyperbolic and Spherical Tiling Gallery
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
- Hyperbolic Planar Tessellations, Don Hatch
