Order-7 triangular tiling
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Order-7 triangular tiling | |
---|---|
Rank | 3 |
Type | Regular |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Hetrat |
Coxeter diagram | o7o3x () |
Schläfli symbol | {3,7} |
Elements | |
Faces | 14N Triangles |
Edges | 21N |
Vertices | 6N |
Vertex figure | Heptagon, edge length 1 |
Holes | 6N Heptagons |
Measures (edge length 1) | |
Circumradius | |
Related polytopes | |
Army | Hetrat |
Regiment | Hetrat |
Dual | Heptagonal tiling |
φ 2 | Order-7/2 heptagonal tiling |
Abstract & topological properties | |
Surface | Sphere |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | [7,3] |
Convex | Yes |
The order-7 triangular tiling or hetrat is a regular tiling of the hyperbolic plane. 7 triangles join at each vertex.
It is the first regular tiling of triangles to be hyperbolic, rather than spherical or Euclidean.
Related polytopes[edit | edit source]
This tiling shares its edges with the great heptagonal tiling.
External links[edit | edit source]
- Klitzing, Richard. "Hetrat".
- Nan Ma. "Order-7 triangular tiling {3,7}".
- Wikipedia contributors. "Order-7 triangular tiling".