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Order-4 square hosohedral honeycomb

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Order-4 square hosohedral honeycomb
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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. In other words, it is a packing of infinitely tall square columns. 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.

Order-4 square hosohedral honeycomb
Thumb
Centrally projected onto a sphere
TypeDegenerate regular honeycomb
Schläfli symbol{2,4,4}
Coxeter diagrams
Cells{2,4}
Faces{2}
Edge figure{4}
Vertex figure{4,4}
DualOrder-2 square tiling honeycomb
Coxeter group[2,4,4]
PropertiesRegular
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Images

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

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Centered on pole
Thumb
Centered on equator
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Perspective

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

More information Space, E3 ...

Truncated order-4 square hosohedral honeycomb

More information Order-2 square tiling honeycombTruncated order-4 square hosohedral honeycomb Partial tessellation with alternately colored cubes ...

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.

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See also

References

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