Truncated order-6 pentagonal tiling | |
---|---|
Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex configuration | 6.10.10 |
Schläfli symbol | t{5,6} t(5,5,3) |
Wythoff symbol | 2 6 | 5 3 5 5 | |
Coxeter diagram | |
Symmetry group | [6,5], (*652) [(5,5,3)], (*553) |
Dual | Order-5 hexakis hexagonal tiling |
Properties | Vertex-transitive |
In geometry, the truncated order-6 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1,2{6,5}.
Uniform colorings[edit]
t012(5,5,3) |
With mirrors |
An alternate construction exists from the [(5,5,3)] family, as the omnitruncation t012(5,5,3). It is shown with two (colors) of decagons. |
Symmetry[edit]
The dual of this tiling represents the fundamental domains of the *553 symmetry. There are no mirror removal subgroups of [(5,5,3)], but this symmetry group can be doubled to 652 symmetry by adding a bisecting mirror to the fundamental domains.
Type | Reflective domains | Rotational symmetry |
---|---|---|
Index | 1 | 2 |
Diagram | ||
Coxeter (orbifold) |
[(5,5,3)] = (*553) |
[(5,5,3)]+ = (553) |
Related polyhedra and tiling[edit]
Uniform hexagonal/pentagonal tilings | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Symmetry: [6,5], (*652) | [6,5]+, (652) | [6,5+], (5*3) | [1+,6,5], (*553) | ||||||||
{6,5} | t{6,5} | r{6,5} | 2t{6,5}=t{5,6} | 2r{6,5}={5,6} | rr{6,5} | tr{6,5} | sr{6,5} | s{5,6} | h{6,5} | ||
Uniform duals | |||||||||||
V65 | V5.12.12 | V5.6.5.6 | V6.10.10 | V56 | V4.5.4.6 | V4.10.12 | V3.3.5.3.6 | V3.3.3.5.3.5 | V(3.5)5 |
References[edit]
- 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.
Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
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