Stellated heptagonal tiling

Stellated heptagonal tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Sheat
Coxeter diagram	x7/2o7o ()
Schläfli symbol	{7/2, 7}
Elements
Faces	2N heptagrams
Edges	7N
Vertices	2N
Vertex figure	Heptagon, edge length 2cos(2π/7)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{1-\cos^2\frac{\pi}{7}}{1-2\cos\frac{\pi}{7}}} ≈ 0.48451 i$
Central density	3
Related polytopes
Army	Hetrat
Regiment	Sheat
Dual	Great heptagonal tiling
Convex core	Heptagonal tiling
Topological properties
Orientable	Yes
Properties
Symmetry	[7,3]
Convex	No

The stellated heptagonal tiling or sheat, also known as the heptagrammic tiling or order-7 heptagrammic tiling, is a regular star tiling of the hyperbolic plane. 7 heptagrams join at each vertex.

As the name suggests, it is a stellation of the heptagonal tiling. It is related to the spherical small stellated dodecahedron, which can be obtained from a similar stellation of the regular dodecahedron.

External links

• Klitzing, Richard. "x7/2o7o".

• Wikipedia Contributors. "Order-7 heptagrammic tiling".
• Nan Ma. "Order-7 heptagrammic tiling {7/2,7}".