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 |
Abstract & 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.
As with other regular polyhedra with Schläfli symbols of the form {p,4}, it can also be constructed as the rectification of {p,p}, in this case 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]
Notable quotients[edit | edit source]
The order-4 apeirogonal tiling is the universal cover of several regular skew polyhedra:
- The Petrial square tiling and the blended Petrial square tiling, both , are quotients of order-4 apeirogonal tiling along its Petrie polygons.
- The Petrial muoctahedron, , is a quotient of order-4 apeirogonal tiling along both its Petrie polygons and its 2-zigzags.
- The skewed muoctahedron, , is a quotient of the order-4 apeirogonal tiling along the 2-zigzags of its dual.
- The helical square tiling is a quotient of the order-4 apeirogonal tiling.
- The Petrial helical square tiling is a quotient of the order-4 apeirogonal tiling.
External links[edit | edit source]
- Klitzing, Richard. "squazat".
- Wikipedia contributors. "Order-4 apeirogonal tiling".