- Source: Infinite-order triangular tiling
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)}, . 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.
Related polyhedra and tiling
This tiling is topologically related as part of a sequence of regular polyhedra with Schläfli symbol {3,p}.
= 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, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
"Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.
External links
Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Infinite-order triangular tiling
- Truncated infinite-order triangular tiling
- Order-7 tetrahedral honeycomb
- Triangular tiling
- Order-6-4 triangular honeycomb
- Order-infinite-3 triangular honeycomb
- Order-3-7 heptagonal honeycomb
- Order-6 tetrahedral honeycomb
- Order-6 hexagonal tiling honeycomb
- Order-3-7 hexagonal honeycomb
