# Square tiling honeycomb

Square tiling honeycomb
Rank4
TypeRegular, paracompact
SpaceHyperbolic
Notation
Bowers style acronymSquah
Coxeter diagramx4o4o3o ()
Schläfli symbol{4,4,3}
Elements
Cells6N square tilings
Faces3NM squares
Edges4NM
VerticesNM
Vertex figureCube, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {i{\sqrt {2}}}{2}}\approx 0.70711i}$
Related polytopes
ArmySquah
RegimentSquah
DualOctahedral honeycomb
Abstract & topological properties
Flag count48NM
OrientableYes
Properties
Symmetry[4,4,3]
ConvexYes

The order-3 square tiling honeycomb or just square tiling honeycomb is a paracompact regular tiling of 3D hyperbolic space. Each cell is a square tiling whose vertices lie on a horosphere, a surface in hyperbolic space that approaches a single ideal point at infinity. 3 square tilings meet at each edge, and 6 meet at each vertex.

It can be formed by rectifying the order-4 square tiling honeycomb.

## Representations

The square tiling honeycomb has the following Coxeter diagrams:

• x4o4o3o () (full symmetry)
• o4x4o4o () (as rectified order-4 square tiling honeycomb)
• o4x4o2o4*b () (cuboid verf)
• x4o4x2o4*b () (square frustum verf)
• x4o4x4o4*a () (rectangular frustum verf)