Order-6 triangular hosohedral honeycomb | |
---|---|
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.
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,
.
Order-6 triangular hosohedral honeycomb | |
---|---|
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.
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,
.