# Order-5 pentagonal tiling

Order-5 pentagonal tiling Rank3
TypeRegular
SpaceHyperbolic
Notation
Bowers style acronymPepat
Coxeter diagramx5o5o (     )
Schläfli symbol{5,5}
Elements
Faces2N pentagons
Edges5N
Vertices2N
Vertex figurePentagon, edge length (1+5)/2
Measures (edge length 1)
Circumradius$\sqrt{-\frac{\sqrt5}{8}} ≈ 0.52869 i$ Related polytopes
ArmyPepat
RegimentPepat
DualOrder-5 pentagonal tiling
Topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[5,5]
ConvexYes

The order-5 pentagonal tiling or pepat is a regular tiling of the hyperbolic plane. 5 pentagons join at each vertex. It is self-dual.

It is the simplest self-dual regular hyperbolic tiling.

It can be formed by alternating the order-5 square tiling.

## Representations

The order-5 pentagonal tiling has the following Coxeter diagrams:

## Related polytopes

Two uniform polyhedra, the dodecadodecahedron and the ditrigonary dodecadodecahedron, along with their duals, the medial rhombic triacontahedron and medial triambic icosahedron, are quotients of this tiling.