Heptagrammic-order heptagonal tiling
{{Uniform hyperbolic tiles db|Reg hyperbolic tiling stat table|U7H_0}}
In geometry, the heptagrammic-order heptagonal tiling is a regular star-tiling of the hyperbolic plane. It has Schläfli symbol of {7,7/2}. The vertex figure heptagrams are {7/2}, 40px. The heptagonal faces overlap with density 3.
Related tilings
It has the same vertex arrangement as the regular order-7 triangular tiling, {3,7}. The full set of edges coincide with the edges of a heptakis heptagonal tiling.
It is related to a Kepler-Poinsot polyhedron, the great dodecahedron, {5,5/2}, which is polyhedron and a density-3 regular star-tiling on the sphere (resembling a regular icosahedron in this state, similarly to this tessellation resembling the order-7 triangular tiling):
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, {{ISBN|978-1-56881-220-5}} (Chapter 19, The Hyperbolic Archimedean Tessellations)
- {{Cite book|title=The Beauty of Geometry: Twelve Essays|year=1999|publisher=Dover Publications|lccn=99035678|isbn=0-486-40919-8|chapter=Chapter 10: Regular honeycombs in hyperbolic space}}
External links
- {{MathWorld | urlname= HyperbolicTiling | title = Hyperbolic tiling}}
- {{MathWorld | urlname=PoincareHyperbolicDisk | title = Poincaré hyperbolic disk }}
{{Tessellation}}
Category:Heptagrammic-order tilings
{{hyperbolic-geometry-stub}}