Cairo pentagonal tiling

Cairo pentagonal tiling
Rank	3
Type	Uniform dual
Space	Euclidean
Notation
Coxeter diagram	p4p4o ()
Elements
Faces	2N mirror-symmetric pentagons
Edges	N+4N
Vertices	N+2N
Vertex figure	N squares, 2N triangles
Related polytopes
Dual	Snub square tiling
Conjugate	Cairo pentagrammic tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	R3/2
Convex	Yes
Nature	Tame

The Cairo pentagonal tiling is an isohedral tiling with mirror-symmetric pentagons for faces, joining 3 or 4 to a vertex. It is the dual of the uniform snub square tiling.

Each face of this tiling is a bilaterally-symmetric pentagon with 1 short and 4 long edges. If the short edge has length 1, the long edges have length ${\frac {1+{\sqrt {3}}}{2}}\approx 1.36603$. Two non-adjacent angles measure 90°, while the other three angles measure 120°.

External links

• Wikipedia contributors. "Cairo pentagonal tiling".