Heptagonal tiling

Heptagonal tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Heat
Coxeter diagram	x7o3o ()
Schläfli symbol	{7,3}
Elements
Faces	6N Heptagons
Edges	21N
Vertices	14N
Vertex figure	Triangle, edge length 2cos(π/7)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3}{12-16\cos^2\frac{\pi}{7}}} ≈ 1.74261 i$
Related polytopes
Army	Heat
Regiment	Heat
Dual	Order-7 triangular tiling
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[7,3]
Convex	Yes

The order-3 heptagonal tiling, or just heptagonal tiling or heat, is a regular tiling of the hyperbolic plane. 3 heptagons join at each vertex.

This tiling is the simplest tiling with three regular polygons at each vertex that neither fits in Euclidean space like the hexagonal tiling does, nor folds into spherical space like the dodecahedron (pentagons), cube (squares), or tetrahedron (triangles).

Related polytopes

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

• Wikipedia Contributors. "Heptagonal tiling".
• Nan Ma. "Heptagonal tiling {7,3}".