Order-4 apeirogonal tiling
Jump to navigation
Jump to search
| Order-4 apeirogonal tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular, paracompact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Squazat |
| Coxeter diagram | x∞o4o (    ) |
| Schläfli symbol | {∞,4} |
| Elements | |
| Faces | 4N apeirogons |
| Edges | 2NM |
| Vertices | NM |
| Vertex figure | Square, edge length 2 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Squazat |
| Regiment | Squazat |
| Dual | Order-∞ square tiling |
| Topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | [∞,4] |
| Convex | Yes |
The order-4 apeirogonal tiling is a paracompact regular tiling of the hyperbolic plane. 4 apeirogons join at each vertex.
It can be formed by rectifying the order-∞ apeirogonal tiling.
Representations[edit | edit source]
The order-4 apeirogonal tiling has the following Coxeter diagrams:
- x∞o4o (full symmetry)
- o∞x∞o () (as rectified order-∞ apeirogonal tiling)
- x∞x∞o∞*a (three types of faces) (
)
Related polytopes[edit | edit source]
| Name | OBSA | Schläfli symbol | CD diagram | Picture |
|---|---|---|---|---|
| Order-4 apeirogonal tiling | squazat | {∞,4} |
|
|
| Truncated order-4 apeirogonal tiling | tosquazat | t{∞,4} |
|
 |
| Tetraapeirogonal tiling | tezt | r{∞,4} |
|
 |
| Truncated order-∞ square tiling | tazsquat | t{4,∞} |
|
 |
| Order-∞ square tiling | azsquat | {4,∞} |
|
 |
| Small rhombitetraapeirogonal tiling | srotezt | rr{∞,4} |
|
 |
| Great rhombitetraapeirogonal tiling | grotezt | tr{∞,4} |
|
 |
| Snub tetraapeirogonal tiling | sr{∞,4} | 
|
 |
External links[edit | edit source]
- Klitzing, Richard. "squazat".
- Wikipedia Contributors. "Order-4 apeirogonal tiling".