Order-9 triangular tiling

Order-9 triangular tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Entrat
Coxeter diagram	o9o3x ()
Schläfli symbol	{3,9}
Elements
Faces	6N triangles
Edges	9N
Vertices	2N
Vertex figure	Enneagon, edge length 1
Measures (edge length 1)
Circumradius	$\sqrt{\frac{1-\cos^2\frac{\pi}{9}}{3-4\cos^2\frac{\pi}{9}}} ≈ 0.46888 i$
Related polytopes
Army	Entrat
Regiment	Entrat
Dual	Enneagonal tiling
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[9,3]
Convex	Yes

The order-9 triangular tiling is a regular tiling of the hyperbolic plane. 9 triangles join at each vertex.

Related polytopes

o9o3o truncations

Name	OBSA	Schläfli symbol	CD diagram	Picture
Enneagonal tiling	enat	{9,3}	x9o3o
Truncated enneagonal tiling	tenat	t{9,3}	x9x3o	File:X9x3o hr.png
Trienneagonal tiling	tent	r{9,3}	o9x3o	File:O9x3o hr.png
Truncated order-9 triangular tiling	tentrat	t{3,9}	o9x3x	File:O9x3x hr.png
Order-9 triangular tiling	entrat	{3,9}	o9o3x
Small rhombitrienneagonal tiling	srotent	rr{9,3}	x9o3x	File:X9o3x hr.png
Great rhombitrienneagonal tiling	grotent	tr{9,3}	x9x3x
Snub trienneagonal tiling	snatent	sr{9,3}	s9s3s	File:S9s3s hr.png