Pentaapeirogonal tiling

Pentaapeirogonal tiling
Rank	3
Type	Uniform, paracompact
Space	Hyperbolic
Notation
Bowers style acronym	Pazt
Coxeter diagram	o∞x5o ()
Elements
Faces	2NM pentagons, 10N Apeirogons
Edges	10NM
Vertices	5NM
Vertex figure	Rectangle, edge lengths (1+√5)/2 and 2
Measures (edge length 1)
Circumradius	${\frac {i({\sqrt {5}}-1)}{2}}\approx 0.61803i$
Related polytopes
Army	Pazt
Regiment	Pazt
Dual	∞-5 rhombille tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[∞,5]
Convex	Yes

The pentaapeirogonal tiling, or pazt, is a paracompact uniform tiling of the hyperbolic plane. 2 apeirogons and 2 pentagons join at each vertex. It can be formed from the rectification of either the order-5 apeirogonal tiling or its dual order-∞ pentagonal tiling.

Representations

The tetraapeirogonal tiling has the following Coxeter diagrams:

• o∞x5o () (full symmetry)
• o5x∞x5*a () (half symmetry, 2 types of pentagons)