# Snub square tiling

Snub square tiling
Rank3
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymSnasquat
Coxeter diagrams4s4o ()
Elements
Faces2N triangles, N squares
EdgesN+4N
Vertices2N
Vertex figureIrregular pentagon, edge lengths 1, 1, 2, 1, 2
Measures (edge length 1)
Vertex density${\displaystyle 4(2-\sqrt3) \approx 1.07180}$
Related polytopes
ArmySnasquat
RegimentSnasquat
DualCairo pentagonal tiling
ConjugateRetrosnub square tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[4+, 4]
ConvexYes

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