Order-6 triangular hosohedral honeycomb explained

bgcolor=#e7dcc3 colspan=2	Order-6 triangular hosohedral honeycomb
Type	Degenerate regular honeycomb
Schläfli symbol
Coxeter diagrams
Cells
Faces
Edge figure
Vertex figure
Dual	Order-2 hexagonal tiling honeycomb
Coxeter group	[2,3,6]
Properties	Regular

In geometry, the order-6 triangular hosohedral honeycomb a regular space-filling tessellation (or honeycomb) with Schläfli symbol . It has 6 triangular hosohedra 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 triangular tiling is seen on each hemisphere.

Images

Stereographic projections of central spherical projection, with all edges being projected into circles. Seen below triangular tiling edges are colored into 3 parallel sets for each hemisphere.

Related honeycombs

This honeycomb can be truncated as t or ×, Coxeter diagram, seen as one layer of triangular prisms, within a triangular prismatic honeycomb, .

See also

• Order-7 tetrahedral honeycomb
• List of regular polytopes

References

• The Beauty of Geometry: Twelve Essays (1999), Dover Publications,, (Chapter 10, Regular Honeycombs in Hyperbolic Space)