In geometry, the truncated order-4 heptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{7,4}.

Truncated heptagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	4.14.14
Schläfli symbol	t{7,4}
Wythoff symbol	2 4 | 7 2 7 7 |
Coxeter diagram	or
Symmetry group	[7,4], (*742) [7,7], (*772)
Dual	Order-7 tetrakis square tiling
Properties	Vertex-transitive

There are two uniform constructions of this tiling, first by the [7,4] kaleidoscope, and second by removing the last mirror, [7,4,1⁺], gives [7,7], (*772).

More information Name, Tetraheptagonal ...

Two uniform constructions of 4.7.4.7

Name	Tetraheptagonal	Truncated heptaheptagonal
Image
Symmetry	[7,4] (*742)	[7,7] = [7,4,1+] (*772) =
Symbol	t{7,4}	tr{7,7}
Coxeter diagram

Close

There is only one simple subgroup [7,7]⁺, index 2, removing all the mirrors. This symmetry can be doubled to 742 symmetry by adding a bisecting mirror.

More information Type, Reflectional ...

Small index subgroups of [7,7]

Type	Reflectional	Rotational
Index	1	2
Diagram
Coxeter (orbifold)	[7,7] = (*772)	[7,7]+ = (772)

Close

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
• "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

Wikimedia Commons has media related to Uniform tiling 4-14-14.

• Uniform tilings in hyperbolic plane
• List of regular polytopes

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

This hyperbolic geometry-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e