Rhombitetraheptagonal tiling
Rhombitetraheptagonal tiling | |
---|---|
![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex figure | 4.4.7.4 |
Schläfli symbol | rr{7,4} |
Wythoff symbol | 4 | 7 2 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [7,4], (*742) |
Dual | Deltoidal tetraheptagonal tiling |
Properties | Vertex-transitive |
In geometry, the rhombitetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of rr{4,7}. It can be seen as constructed as a rectified tetraheptagonal tiling, r{7,4}, as well as an expanded order-4 heptagonal tiling or expanded order-7 square tiling.
Dual tiling
The dual is called the deltoidal tetraheptagonal tiling with face configuration V.4.4.4.7.
Related polyhedra and tiling
Symmetry [n,4], (*n42) |
Spherical | Euclidean | Compact hyperbolic | Paracompact | |||
---|---|---|---|---|---|---|---|
*342 [3,4] |
*442 [4,4] |
*542 [5,4] |
*642 [6,4] |
*742 [7,4] |
*842 [8,4] |
*∞42 [∞,4] | |
Expanded figures |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
Coxeter Schläfli |
![]() ![]() ![]() ![]() ![]() rr{3,4} |
![]() ![]() ![]() ![]() ![]() rr{4,4} |
![]() ![]() ![]() ![]() ![]() rr{5,4} |
![]() ![]() ![]() ![]() ![]() rr{6,4} |
![]() ![]() ![]() ![]() ![]() rr{7,4} |
![]() ![]() ![]() ![]() ![]() rr{8,4} |
![]() ![]() ![]() ![]() ![]() rr{∞,4} |
Dual (rhombic) figures configuration |
![]() V3.4.4.4 |
![]() V4.4.4.4 |
![]() 5.4.4.4 |
![]() V6.4.4.4 |
![]() V7.4.4.4 |
![]() V8.4.4.4 |
![]() V∞.4.4.4 |
Coxeter | ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
Symmetry: [7,4], (*742) | [7,4]+, (742) | [7+,4], (7*2) | [7,4,1+], (*772) | |||||||
---|---|---|---|---|---|---|---|---|---|---|
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() | |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() | |
{7,4} | t{7,4} | r{7,4} | 2t{7,4}=t{4,7} | 2r{7,4}={4,7} | rr{7,4} | tr{7,4} | sr{7,4} | s{7,4} | h{4,7} | |
Uniform duals | ||||||||||
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() | |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() | |||
V74 | V4.14.14 | V4.7.4.7 | V7.8.8 | V47 | V4.4.7.4 | V4.8.14 | V3.3.4.3.7 | V3.3.7.3.7 | V77 |
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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.
See also
![]() |
Wikimedia Commons has media related to Uniform tiling 4-4-4-7. |
- Uniform tilings in hyperbolic plane
- List of regular polytopes
External links
- Weisstein, Eric W., "Hyperbolic tiling", MathWorld.
- Weisstein, Eric W., "Poincaré hyperbolic disk", MathWorld.
- Hyperbolic and Spherical Tiling Gallery
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
- Hyperbolic Planar Tessellations, Don Hatch
|