# Square tiling prism

Square tiling prism
Rank4
TypeUniform
SpaceEuclidean
Notation
Coxeter diagram
Elements
CellsMN cubes, 2 square tilings
Faces2MN+2MN squares
EdgesMN+4MN
Vertices2MN
Vertex figureSquare pyramid
Related polytopes
Army*
Regiment*
DualSquare tiling tegum
Topological properties
OrientableYes
Properties
SymmetryR3×A1
ConvexYes

The square tiling prism or cubic slab honeycomb is a prismatic uniform honeycomb of the Euclidean plane. It consists of 2 square tilings and ∞ cubes. Each vertex joins 1 square tiling and 4 cubes. It is a prism based on the square tiling.

It appears as a segment of the cubic honeycomb.

## Vertex coordinates

A square tiling prism of edge length 1 has vertex coordinates given by, where ${\displaystyle i,\,j}$ range over the integers:

• ${\displaystyle \left(±\tfrac12,\,i,\,j,\,0\right)}$

## Semi-uniform variant

The apeirogonal prism has a semi-uniform variant of the form x y4o4o that maintains its full symmetry. This variant uses square prisms as its sides.