# Order-4 square hosohedral honeycomb

(Redirected from Cubic prismatic slab honeycomb)
Order-4 square hosohedral honeycomb

Centrally projected onto a sphere
Type Degenerate regular honeycomb
Schläfli symbol {2,4,4}
Coxeter diagrams
Cells {2,4}
Faces {2}
Edge figure {4}
Vertex figure {4,4}
Dual {4,4,2}
Coxeter group [2,4,4]
Properties Regular

In geometry, the order-4 square hosohedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {2,4,4}. It has 4 square hosohedra {2,4} around each edge. It is a degenerate honeycomb in Euclidean space, but can be seen as a projection onto the sphere. Its vertex figure, a square tiling is seen on each hemisphere.

## Images

Stereographic projections of spherical projection, with all edges being projected into circles.

 Centered on pole Centered on equator

## Related honeycombs

It is a part of a sequence of honeycombs with a square tiling vertex figure:

### Truncated order-4 square hosohedral honeycomb

Order-2 square tiling honeycomb
Truncated order-4 square hosohedral honeycomb

Partial tessellation with alternately colored cubes
Type uniform convex honeycomb
Schläfli symbol {4,4}×{}
Coxeter diagrams

Cells {3,4}
Faces {4}
Vertex figure Square pyramid
Dual
Coxeter group [2,4,4]
Properties Uniform

The {2,4,4} honeycomb can be truncated as t{2,4,4} or {}×{4,4}, Coxeter diagram , seen as a layer of cubes, partially shown here with alternately colored cubic cells. Thorold Gosset identified this semiregular infinite honeycomb as a cubic semicheck.

The alternation of this honeycomb, , consists of infinite square pyramids and infinite tetrahedrons, between 2 square tilings.