Order-5 pentagonal tiling

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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
Related polytopes
ArmyPepat
RegimentPepat
DualOrder-5 pentagonal tiling
Abstract & 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[edit | edit source]

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

Related polytopes[edit | edit source]

It is isomorphic to the universal cover of the great dodecahedron and small stellated dodecahedron.

External links[edit | edit source]