Heptagrammic-order heptagonal tiling

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}, . The heptagonal faces overlap with density 3.

Heptagrammic-order heptagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic regular tiling
Vertex configuration	77/2
Schläfli symbol	{7,7/2}
Wythoff symbol	7/2 | 7 2
Coxeter diagram
Symmetry group	[7,3], (*732)
Dual	Order-7 heptagrammic tiling
Properties	Vertex-transitive, edge-transitive, face-transitive

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)
• "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

External links

• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.