Order-6 triangular hosohedral honeycomb

Order-6 triangular hosohedral honeycomb
Type	Degenerate regular honeycomb
Schläfli symbol	{2,3,6}
Coxeter diagrams	File:CDel node 1.pngFile:CDel 2.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 6.pngFile:CDel node.png
Cells	{2,3} File:Spherical trigonal hosohedron.svg
Faces	{2}
Edge figure	{6}
Vertex figure	{3,6} File:Uniform tiling 63-t2-red.svg
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 {2,3,6}. It has 6 triangular hosohedra {2,3} 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.

File:Order-6 triangular hosohedral honeycomb.png Centered on pole

File:Order-6 triangular hosohedral honeycomb2.png Centered on equator

Related honeycombs

This honeycomb can be truncated as t{2,3,6} or {}×{3,6}, Coxeter diagram File:CDel node 1.pngFile:CDel 2.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 6.pngFile:CDel node.png, seen as one layer of triangular prisms, within a triangular prismatic honeycomb, File:CDel node 1.pngFile:CDel infin.pngFile:CDel node.pngFile:CDel 2.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 6.pngFile:CDel node.png.

File:Triangular prismatic honeycomb.svg

See also

• Order-7 tetrahedral honeycomb
• List of regular polytopes

References

• The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, (Chapter 10, Regular Honeycombs in Hyperbolic Space Archived 2016-06-10 at the Wayback Machine)