Order-∞ pentagonal tiling
Jump to navigation
Jump to search
Order-∞ pentagonal tiling | |
---|---|
Rank | 3 |
Type | Regular, paracompact |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Azpat |
Coxeter diagram | o∞o5x () |
Schläfli symbol | {5,∞} |
Elements | |
Faces | 2NM pentagons |
Edges | 5NM |
Vertices | 10N |
Vertex figure | Apeirogon, edge length (1+√5)/2 |
Measures (edge length 1) | |
Circumradius | |
Related polytopes | |
Army | Azpat |
Regiment | Azpat |
Dual | Order-5 apeirogonal tiling |
Abstract & topological properties | |
Surface | Sphere |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | [∞,5] |
Convex | Yes |
The order-∞ pentagonal tiling or infinite-order pentagonal tiling is a paracompact regular tiling of the hyperbolic plane. Infinitely many ideal pentagons join at each vertex. All vertices are ideal points at infinity.
Representations[edit | edit source]
An order–∞ pentagonal tiling has the following Coxeter diagrams:
- o∞o5x () (full symmetry)
- x5o∞o5*a () (pentagons of two types)
External links[edit | edit source]
- Wikipedia contributors. "Infinite-order pentagonal tiling".