Order-7 triangular tiling

Order-7 triangular tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Hetrat
Coxeter diagram	o7o3x ()
Schläfli symbol	{3,7}
Elements
Faces	14N Triangles
Edges	21N
Vertices	6N
Vertex figure	Heptagon, edge length 1
Measures (edge length 1)
Circumradius	$\sqrt{\frac{1-\cos^2\frac{\pi}{7}}{3-4\cos^2\frac{\pi}{7}}} ≈ 0.87306 i$
Related polytopes
Army	Hetrat
Regiment	Hetrat
Dual	Heptagonal tiling
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[7,3]
Convex	Yes

The order-7 triangular tiling or hetrat is a regular tiling of the hyperbolic plane. 7 triangles join at each vertex.

It is the first tiling of triangles to be hyperbolic, rather than spherical or Euclidean.

Related polytopes

This tiling shares its edges with the great heptagonal tiling.

o7o3o truncations

Name	OBSA	Schläfli symbol	CD diagram	Picture
Heptagonal tiling	heat	{7,3}	x7o3o
Truncated heptagonal tiling	theat	t{7,3}	x7x3o
Triheptagonal tiling	thet	r{7,3}	o7x3o
Truncated order-7 triangular tiling	thetrat	t{3,7}	o7x3x
Order-7 triangular tiling	hetrat	{3,7}	o7o3x
Small rhombitriheptagonal tiling	srothet	rr{7,3}	x7o3x
Great rhombitriheptagonal tiling	grothet	tr{7,3}	x7x3x
Snub triheptagonal tiling	snathet	sr{7,3}	s7s3s

External links

• Klitzing, Richard. "Hetrat".

• Nan Ma. "Order-7 triangular tiling {3,7}".

• Wikipedia Contributors. "Order-7 triangular tiling".