Snub square tiling

Snub square tiling
Rank	3
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Snasquat
Coxeter diagram	s4s4o ()
Elements
Faces	2N triangles, N squares
Edges	N+4N
Vertices	2N
Vertex figure	Irregular pentagon, edge lengths 1, 1, √2, 1, √2
Measures (edge length 1)
Vertex density	$4(2-\sqrt3) \approx 1.07180$
Related polytopes
Army	Snasquat
Regiment	Snasquat
Dual	Cairo pentagonal tiling
Conjugate	Retrosnub square tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[4+, 4]
Convex	Yes

The snub square tiling, or snasquat, is one of the eleven convex uniform tilings of the Euclidean plane. 3 snub triangles and 2 squares join at each vertex of this tiling. It can be formed by alternating the truncated square tiling and adjusting to make all edge lengths equal.

Representations

A snub square tiling has the following Coxeter diagrams:

• s4s4o (full symmetry)
• s4s4s (as alternated omnitruncated square tiling)

Related tilings

o4o4o truncations

Name	OBSA	Schläfli symbol	CD diagram	Picture
Square tiling	squat	{4,4}	x4o4o
Truncated square tiling	tosquat	t{4,4}	x4x4o
Rectified square tiling = Square tiling	squat	r{4,4}	o4x4o
Truncated square tiling	tosquat	t{4,4}	o4x4x
Square tiling	squat	{4,4}	o4o4x
Cantellated square tiling = Square tiling	squat	rr{4,4}	x4o4x
Omnitruncated square tiling = Truncated square tiling	tosquat	tr{4,4}	x4x4x
Snub square tiling	snasquat	sr{4,4}	s4s4s

External links

• Klitzing, Richard. "snasquat".

• Wikipedia Contributors. "Snub square tiling".