Английская Википедия:Infinite-order triangular tiling
Шаблон:Uniform hyperbolic tiles db
In geometry, the infinite-order triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of {3,∞}. All vertices are ideal, located at "infinity" and seen on the boundary of the Poincaré hyperbolic disk projection.
Symmetry
A lower symmetry form has alternating colors, and represented by cyclic symbol {(3,∞,3)}, Шаблон:CDD. The tiling also represents the fundamental domains of the *∞∞∞ symmetry, which can be seen with 3 colors of lines representing 3 mirrors of the construction.
| Файл:Infinite-order triangular tiling.svg Alternated colored tiling |
Файл:Iii symmetry mirrors.png *∞∞∞ symmetry |
Файл:Apolleangasket symmetry.png Apollonian gasket with *∞∞∞ symmetry |
Related polyhedra and tiling
This tiling is topologically related as part of a sequence of regular polyhedra with Schläfli symbol {3,p}. Шаблон:Triangular regular tiling
Шаблон:Order i-3 tiling table Шаблон:Order i-3-3 tiling table
Other infinite-order triangular tilings
A nonregular infinite-order triangular tiling can be generated by a recursive process from a central triangle as shown here:
See also
- Infinite-order tetrahedral honeycomb
- List of regular polytopes
- List of uniform planar tilings
- Tilings of regular polygons
- Triangular tiling
- Uniform tilings in hyperbolic plane
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, Шаблон:ISBN (Chapter 19, The Hyperbolic Archimedean Tessellations)
- Шаблон:Cite book
External links
- Английская Википедия
- Страницы с неработающими файловыми ссылками
- Hyperbolic tilings
- Infinite-order tilings
- Isogonal tilings
- Isohedral tilings
- Regular tilings
- Triangular tilings
- Страницы, где используется шаблон "Навигационная таблица/Телепорт"
- Страницы с телепортом
- Википедия
- Статья из Википедии
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