Order-5 square tiling

Order-5 square tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Pesquat
Coxeter diagram	o5o4x ()
Schläfli symbol	{4,5}
Elements
Faces	5N Squares
Edges	10N
Vertices	4N
Vertex figure	Pentagon, edge length √2
Measures (edge length 1)
Circumradius	$\frac{i\sqrt[4]{5}}{2} ≈ 0.74767 i$
Related polytopes
Army	Pesquat
Regiment	Pesquat
Dual	Pentagonal tiling
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[5,4]
Convex	Yes

The order-5 square tiling or pesquat is a regular tiling of the hyperbolic plane. 5 squares join at each vertex.

This tiling can be alternated to produce the regular order-5 pentagonal tiling.

Related polytopes

o5o4o truncations

Name	OBSA	Schläfli symbol	CD diagram	Picture
Pentagonal tiling	peat	{5,4}	x5o4o
Truncated pentagonal tiling	topeat	t{5,4}	x5x4o
Tetrapentagonal tiling	tepet	r{5,4}	o5x4o
Truncated order-5 square tiling	topesquat	t{4,5}	o5x4x
Order-5 square tiling	pesquat	{4,5}	o5o4x
Small rhombitetrapentagonal tiling	srotepet	rr{5,4}	x5o4x
Great rhombitetrapentagonal tiling	grotepet	tr{5,4}	x5x4x
Snub tetrapentagonal tiling	stepet	sr{5,4}	s5s4s

External links

• Klitzing, Richard. "Pesquat".

• Wikipedia Contributors. "Order-5 square tiling".