Order-6 pentagonal tiling

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Order-6 pentagonal tiling
Rank3
TypeRegular
SpaceHyperbolic
Notation
Bowers style acronymHipat
Coxeter diagramo6o5x ()
Schläfli symbol{5,6}
Elements
Faces5N pentagons
Edges15N
Vertices6N
Vertex figureHexagon, edge length (1+5)/2
Measures (edge length 1)
Circumradius
Related polytopes
ArmyHipat
RegimentHipat
DualOrder-5 hexagonal tiling
φ 2 Order-3 apeirogonal tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[6,5]
ConvexYes

The order-6 pentagonal tiling is a regular tiling of the hyperbolic plane. 6 pentagons join at each vertex.

Representations[edit | edit source]

The order-6 pentagonal tiling has the following Coxeter diagrams:

  • o6o5x () (main symmetry)
  • o3o5x5*a () (pentagons of two different types)

Related polytopes[edit | edit source]

It is isomorphic to the universal cover of the ditrigonal dodecadodecahedron.

External links[edit | edit source]