Pentagonal tiling

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Pentagonal tiling
Rank3
TypeRegular
SpaceHyperbolic
Notation
Bowers style acronymPeat
Coxeter diagramx5o4o ()
Schläfli symbol{5,4}
Elements
Faces4N Pentagons
Edges10N
Vertices5N
Vertex figureSquare, edge length (1+5)/2
Measures (edge length 1)
Circumradius
Related polytopes
ArmyPeat
RegimentPeat
DualOrder-5 square tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[5,4]
ConvexYes

The order-4 pentagonal tiling, or simply pentagonal tiling or peat, is a regular tiling of the hyperbolic plane. 4 pentagons join at each vertex.

As with other regular polyhedra of the Schläfli symbol {p,4}, it can also be constructed as the rectification of {p,p}, in this case the order-5 pentagonal tiling.

Representations[edit | edit source]

The pentagonal tiling has the following Coxeter diagrams:

Related polytopes[edit | edit source]

It is isomorphic to the universal cover of the dodecadodecahedron.

External links[edit | edit source]