Great enneagonal tiling

Great enneagonal tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Gent
Coxeter diagram	o9/2o9x ()
Schläfli symbol	{9, 9/2}
Elements
Faces	2N enneagons
Edges	9N
Vertices	2N
Vertex figure	Enneagram, edge length 2cos(π/9)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{1-\cos^2\frac{\pi}{9}}{3-4\cos^2\frac{\pi}{9}}} ≈ 0.46888 i$
Central density	3
Related polytopes
Army	Entrat
Regiment	Entrat
Dual	Stellated enneagonal tiling
Convex core	Enneagonal tiling
Topological properties
Orientable	Yes
Properties
Symmetry	[9,3]
Convex	No

The great enneagonal tiling or gent, also known as the enneagrammic-order enneagonal tiling, is a regular star tiling of the hyperbolic plane. 9 enneagons join at each vertex in an enneagrammic arrangement.

It is a faceting of the order-9 triangular tiling, using the bases of its enneagonal pyramid caps as faces. It is related to the spherical great dodecahedron.

External links

• Wikipedia Contributors. "Enneagrammic-order enneagonal tiling".