# 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${\displaystyle {\sqrt {\frac {1-\cos ^{2}{\frac {\pi }{7}}}{3-4\cos ^{2}{\frac {\pi }{7}}}}}\approx 0.87306i}$
Central density3
Related polytopes
ArmyHetrat
RegimentHetrat
DualStellated heptagonal tiling
Convex coreHeptagonal tiling
Abstract & topological properties
Schläfli type{7,7}
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 second-order facetting of the order-7 triangular tiling. It is related to the spherical great dodecahedron, which is the second-order facetting of the regular icosahedron.