# Stellated heptagonal tiling

Stellated heptagonal tiling
Rank3
TypeRegular
SpaceHyperbolic
Notation
Bowers style acronymSheat
Coxeter diagramx7/2o7o ()
Schläfli symbol{7/2, 7}
Elements
Faces2N heptagrams
Edges7N
Vertices2N
Vertex figureHeptagon, edge length 2cos(2π/7)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1-\cos^2\frac{\pi}{7}}{1-2\cos\frac{\pi}{7}}} ≈ 0.48451 i}$
Central density3
Related polytopes
ArmyHetrat
RegimentSheat
DualGreat heptagonal tiling
Convex coreHeptagonal tiling
Topological properties
OrientableYes
Properties
Symmetry[7,3]
ConvexNo

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.