Heptagrammic-order heptagonal tiling

Heptagrammic-order heptagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic regular tiling
Vertex figure	7^7/2
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

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.

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:

John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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.

Periodic

Pythagorean Rhombille Schwarz triangle Rectangle Domino Uniform tiling & honeycomb Coloring Convex Kisrhombille Wallpaper group Wythoff

Aperiodic

Ammann–Beenker Aperiodic set of prototiles List Einstein problem Socolar–Taylor Gilbert Penrose Pentagonal Pinwheel Quaquaversal Rep-tile & Self-tiling Sphinx Truchet

Other

Anisohedral & Isohedral Architectonic & catoptric Circle Limit III Computer graphics Honeycomb Isotoxal Packing Problems Domino Wang Heesch's Squaring Prototile Conway criterion Girih Regular Division of the Plane Regular grid Substitution Voronoi Voderberg

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