Apeirogonal tiling

Apeirogonal tiling
Rank	3
Type	Regular, paracompact
Space	Hyperbolic
Notation
Bowers style acronym	Azat
Coxeter diagram	x∞o3o ()
Schläfli symbol	{∞,3}
Elements
Faces	6N Apeirogons
Edges	3NM
Vertices	2NM
Vertex figure	Triangle, edge length 2
Measures (edge length 1)
Circumradius
Related polytopes
Army	Azat
Regiment	Azat
Dual	Order-∞ triangular tiling
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[∞,3]
Convex	Yes

The order-3 apeirogonal tiling, or just apeirogonal tiling or azat, is a paracompact regular tiling of the hyperbolic plane. 3 apeirogons join at each vertex.

It can be formed by truncating the order-∞ apeirogonal tiling.

Representations[edit | edit source]

The apeirogonal tiling has the following Coxeter diagrams:

x∞o3o (full symmetry)
x∞x∞o (as truncated order-∞ apeirogonal tiling)
x∞x∞x∞*a (three types of faces) ()

Related polytopes[edit | edit source]

o∞o3o truncations
Name	OBSA	Schläfli symbol
Apeirogonal tiling	azat	{∞,3}
Truncated apeirogonal tiling	tazat	t{∞,3}
Triapeirogonal tiling	tazt	r{∞,3}
Truncated order-∞ triangular tiling	taztrat	t{3,∞}
Order-∞ triangular tiling	aztrat	{3,∞}
Small rhombitriapeirogonal tiling	srotazt	rr{∞,3}
Great rhombitriapeirogonal tiling	grotazt	tr{∞,3}
Snub triapeirogonal tiling		sr{∞,3}