# Order-∞ pentagonal tiling

Order-∞ pentagonal tiling Rank3
TypeRegular, paracompact
SpaceHyperbolic
Notation
Bowers style acronymAzpat
Coxeter diagramo∞o5x (     )
Schläfli symbol{5,∞}
Elements
Faces2NM pentagons
Edges5NM
Vertices10N
Vertex figureApeirogon, edge length (1+5)/2
Measures (edge length 1)
Circumradius$0$ Related polytopes
ArmyAzpat
RegimentAzpat
DualOrder-5 apeirogonal tiling
Topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[∞,5]
ConvexYes

The order-∞ pentagonal tiling or infinite-order pentagonal tiling is a paracompact regular tiling of the hyperbolic plane. Infinitely many ideal pentagons join at each vertex. All vertices are ideal points at infinity.

## Representations

An order–∞ pentagonal tiling has the following Coxeter diagrams:

• o∞o5x (full symmetry)
• o5x5o∞*a (pentagons of two types)

## Related polytopes

o∞o5o truncations
Name OBSA Schläfli symbol CD diagram Picture
Order-5 apeirogonal tiling pazat {∞,5}     Truncated order-5 apeirogonal tiling topazat t{∞,5}     Pentaapeirogonal tiling pazt r{∞,5}     Truncated order-∞ pentagonal tiling tazpat t{5,∞}     Order-∞ pentagonal tiling azpat {5,∞}     Small rhombipentaapeirogonal tiling sropazt rr{∞,5}     Great rhombipentaapeirogonal tiling gropazt tr{∞,5}     Snub pentaapeirogonal tiling sr{∞,5}     