Hexaapeirogonal tiling

Hexaapeirogonal tiling
Rank	3
Type	Uniform, paracompact
Space	Hyperbolic
Notation
Bowers style acronym	Hazt
Coxeter diagram	o∞x6o ()
Schläfli symbol	$\left\{{\infty \atop 6}\right\}$
Elements
Faces	NM hexagons, 6N Apeirogons
Edges	6NM
Vertices	3NM
Vertex figure	Rectangle, edge lengths √3 and 2
Measures (edge length 1)
Circumradius	${\frac {i{\sqrt {3}}}{3}}\approx 0.57355i$
Related polytopes
Army	Hazt
Regiment	Hazt
Dual	∞-6 rhombille tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[∞,6]
Convex	Yes

The hexaapeirogonal tiling, or hazt, is a paracompact uniform tiling of the hyperbolic plane. 2 apeirogons and 2 hexagons join at each vertex. It can be formed from the rectification of either the order-6 apeirogonal tiling or its dual order-∞ hexagonal tiling.

Representations

The hexaapeirogonal tiling has the following Coxeter diagrams:

• o∞x6o () (full symmetry)
• o6x∞x6*a () (hexagons of 2 types)
• x3x∞o∞*a () (apeirogons of 2 types)