Truncated tetraheptagonal tiling

Truncated tetraheptagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	4.8.14
Schläfli symbol	tr{7,4} or $t {\begin{matrix} 7 \\ 4 \end{matrix}}$
Wythoff symbol	2 7 4 \|
Coxeter diagram
Symmetry group	[7,4], (*742)
Dual	Order-4-7 kisrhombille tiling
Properties	Vertex-transitive

In geometry, the truncated tetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of tr{4,7}.

Images

Poincaré disk projection, centered on 14-gon:

Symmetry

The dual to this tiling represents the fundamental domains of [7,4] (*742) symmetry. There are three small index subgroups constructed from [7,4] by mirror removal and alternation. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors.

Small index subgroups of [7,4] (*742)
Index	1	2		14
Diagram				File:742 symmetry zz0.png
Coxeter (orbifold)	[7,4] = Error creating thumbnail: Error creating thumbnail: Error creating thumbnail: Error creating thumbnail: (*742)	[7,4,1⁺] = Error creating thumbnail: Error creating thumbnail: Error creating thumbnail: File:CDel node h0.png = Error creating thumbnail: File:CDel split1-77.pngFile:CDel nodeab c1.png (*772)	[7⁺,4] = File:CDel node h2.pngFile:CDel node h2.pngError creating thumbnail: Error creating thumbnail: (7*2)	[7,4] = File:CDel node g.pngFile:CDel 3sg.pngFile:CDel node g.pngError creating thumbnail: Error creating thumbnail: (2222222)
Index	2	4		28
Diagram	File:742 symmetry aaa.png	File:742 symmetry bba.png		File:742 symmetry zza.png
Coxeter (orbifold)	[7,4]⁺ = File:CDel node h2.pngFile:CDel node h2.pngError creating thumbnail: File:CDel node h2.png (742)	[7⁺,4]⁺ = File:CDel node h2.pngFile:CDel node h2.pngError creating thumbnail: File:CDel node h0.png = File:CDel node h2.pngFile:CDel split1-77.pngFile:CDel branch h2h2.pngFile:CDel label2.png (772)		[7*,4]⁺ = File:CDel node g.pngFile:CDel 3sg.pngFile:CDel node g.pngError creating thumbnail: File:CDel node h2.png (2222222)

Related polyhedra and tiling

Template:Order 7-4 tiling table

Template:Omnitruncated4 table Template:Omnitruncated symmetric table

References

John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 Search this book on . (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. Search this book on

External links

Template:Hyperbolic-geometry-stub

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