Order-6 triangular hosohedral honeycomb

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.

Order-6 triangular hosohedral honeycomb
TypeDegenerate regular honeycomb
Schläfli symbol{2,3,6}
Coxeter diagrams
Cells{2,3}
Faces{2}
Edge figure{6}
Vertex figure{3,6}
DualOrder-2 hexagonal tiling honeycomb
Coxeter group[2,3,6]
PropertiesRegular

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.


Centered on pole

Centered on equator

This honeycomb can be truncated as t{2,3,6} or {}×{3,6}, Coxeter diagram , seen as one layer of triangular prisms, within a triangular prismatic honeycomb, .

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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