Pentagonal tiling
(Redirected from Order-4 pentagonal tiling)
Pentagonal tiling | |
---|---|
Rank | 3 |
Type | Regular |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Peat |
Coxeter diagram | x5o4o () |
Schläfli symbol | {5,4} |
Elements | |
Faces | 4N Pentagons |
Edges | 10N |
Vertices | 5N |
Vertex figure | Square, edge length (1+√5)/2 |
Measures (edge length 1) | |
Circumradius | |
Related polytopes | |
Army | Peat |
Regiment | Peat |
Dual | Order-5 square tiling |
Abstract & topological properties | |
Surface | Sphere |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | [5,4] |
Convex | Yes |
The order-4 pentagonal tiling, or simply pentagonal tiling or peat, is a regular tiling of the hyperbolic plane. 4 pentagons join at each vertex.
As with other regular polyhedra of the Schläfli symbol {p,4}, it can also be constructed as the rectification of {p,p}, in this case the order-5 pentagonal tiling.
Representations[edit | edit source]
The pentagonal tiling has the following Coxeter diagrams:
- x5o4o () (full symmetry)
- o5x5o () (as rectified order-5 pentagonal tiling)
Related polytopes[edit | edit source]
It is isomorphic to the universal cover of the dodecadodecahedron.
External links[edit | edit source]
- Klitzing, Richard. "Peat".
- Wikipedia contributors. "Order-4 pentagonal tiling".