# Great heptagonal tiling

Great heptagonal tiling
Rank3
TypeRegular
SpaceHyperbolic
Notation
Bowers style acronymGheat
Coxeter diagramo7/2o7x ()
Schläfli symbol{7, 7/2}
Elements
Faces2N heptagons
Edges7N
Vertices2N
Vertex figureHeptagram, edge length 2cos(π/7)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1-\cos^2\frac{\pi}{7}}{3-4\cos^2\frac{\pi}{7}}} ≈ 0.87306 i}$
Central density3
Related polytopes
ArmyHetrat
RegimentHetrat
DualStellated heptagonal tiling
Convex coreHeptagonal tiling
Topological properties
OrientableYes
Properties
Symmetry[7,3]
ConvexNo

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.