Order-3 heptagonal tiling

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Order-3 heptagonal tiling
Type	Regular tiling
Vertex figure	7.7.7
Schläfli symbol(s)	{7,3}
Wythoff symbol(s)	3 | 7 2
Coxeter-Dynkin(s)
Symmetry	[7,3]
Dual	Order-7 triangular tiling
Properties	Vertex-transitive, edge-transitive, face-transitive
7.7.7
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In geometry, the order-3 heptagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {7,3}.

The image shows a Poincaré disk model projection of the hyperbolic plane.

This tiling is topologically related as a part of sequence of regular polyhedra with vertex figure (n³).

(33)

(43)

(53)

(63) tiling

Contents 1 Wythoff constructions from heptagonal and triangular tilings 2 References 3 See also 4 External links

[edit] Wythoff constructions from heptagonal and triangular tilings

From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling.

Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.

Tiling	Schläfli symbol	Wythoff symbol	Vertex figure	Image
Order-3 heptagonal tiling	t0{7,3}	3 | 7 2	73
Order-3 truncated heptagonal tiling	t0,1{7,3}	2 3 | 7	3.14.14
Rectified order-3 heptagonal tiling (Triheptagonal tiling)	t1{7,3}	2 | 7 3	(3.7)2
Bitruncated order-3 heptagonal tiling (Order-7 truncated triangular tiling)	t1,2{7,3}	2 7 | 3	7.6.6
Order-7 triangular tiling	t2{7,3}	7 | 3 2	37
Cantellated order-3 heptagonal tiling (Small rhombitriheptagonal tiling)	t0,2{7,3}	7 3 | 2	3.4.7.4
Order-3 omnitruncated heptagonal tiling (Great rhombitriheptagonal tiling)	t0,1,2{7,3}	7 3 2 |	4.7.14
Order-3 snub heptagonal tiling	s{7,3}	| 7 3 2	3.3.3.3.7

[edit] References

• Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman and Company. ISBN 0-7167-1193-1. 

[edit] See also

• hexagonal tiling
• Tilings of regular polygons
• List of uniform planar tilings
• List of regular polytopes

[edit] External links

• Eric W. Weisstein, Hyperbolic tiling at MathWorld.
• Eric W. Weisstein, Poincaré hyperbolic disk at MathWorld.
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch