Order-6 triangular hosohedral honeycomb
Order-6 triangular hosohedral honeycomb | |
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Type | Degenerate regular honeycomb |
Schläfli symbol | {2,3,6} |
Coxeter diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | {2,3} ![]() |
Faces | {2} |
Edge figure | {6} |
Vertex figure | {3,6}![]() |
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
[edit]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 |
Related honeycombs
[edit]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
[edit]References
[edit]- The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8 (Chapter 10, Regular Honeycombs in Hyperbolic Space)