Order-4 apeirogonal tiling

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Order-4 apeirogonal tiling
Rank3
TypeRegular, paracompact
SpaceHyperbolic
Notation
Bowers style acronymSquazat
Coxeter diagramx∞o4o ()
Schläfli symbol{∞,4}
Elements
Faces4N apeirogons
Edges2NM
VerticesNM
Vertex figureSquare, edge length 2
Measures (edge length 1)
Circumradius
Related polytopes
ArmySquazat
RegimentSquazat
DualOrder-∞ square tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[∞,4]
ConvexYes

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:

Related polytopes[edit | edit source]

Notable quotients[edit | edit source]

The order-4 apeirogonal tiling is the universal cover of several regular skew polyhedra:

External links[edit | edit source]