Great heptagonal tiling

Great heptagonal tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Gheat
Coxeter diagram	o7/2o7x ()
Schläfli symbol	{7, 7/2}
Elements
Faces	2N heptagons
Edges	7N
Vertices	2N
Vertex figure	Heptagram, edge length 2cos(π/7)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{1-\cos^2\frac{\pi}{7}}{3-4\cos^2\frac{\pi}{7}}} ≈ 0.87306 i$
Central density	3
Related polytopes
Army	Hetrat
Regiment	Hetrat
Dual	Stellated heptagonal tiling
Convex core	Heptagonal tiling
Topological properties
Orientable	Yes
Properties
Symmetry	[7,3]
Convex	No

The great heptagonal tiling or gheat, also known as the heptagrammic-order heptagonal tiling, is a regular star tiling of the hyperbolic plane. 7 heptagons join at each vertex in a heptagrammic arrangement.

It is a faceting of the order-7 triangular tiling, using the bases of its heptagonal pyramid caps as faces. It is related to the spherical great dodecahedron, which can be obtained from a similar faceting of the regular icosahedron.

External links

• Klitzing, Richard. "x7o7/2o".

• Wikipedia Contributors. "Heptagrammic-order heptagonal tiling".
• Nan Ma. "Heptagrammic-order heptagonal tiling {7,7/2}".