Order-6 triangular hosohedral honeycomb

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Order-6 triangular hosohedral honeycomb
Type Degenerate regular honeycomb
Schläfli symbol {2,3,6}
Coxeter diagrams CDel node 1.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 6.pngCDel node.png
Cells {2,3} Spherical trigonal hosohedron.png
Faces {2}
Edge figure {6}
Vertex figure {3,6}
Uniform tiling 63-t2.png
Dual
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.

Order-6 triangular hosohedral honeycomb.png
Centered on pole
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 CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 6.pngCDel node.png, seen as one layer of triangular prisms, within a triangular prismatic honeycomb, CDel node 1.pngCDel infin.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 6.pngCDel node.png.

Triangular prismatic honeycomb.png

See also[]

References[]

  • The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8 (Chapter 10, Regular Honeycombs in Hyperbolic Space)
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