Truncated Order-4 Heptagonal Tiling
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Truncated Order-4 Heptagonal Tiling

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

Constructions

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).

Two uniform constructions of 4.7.4.7
Name Tetraheptagonal Truncated heptahexagonal
Image Uniform tiling 74-t01.png Uniform tiling 77-t012.png
Symmetry [7,4]
(*742)
CDel node c1.pngCDel 7.pngCDel node c2.pngCDel 4.pngCDel node c3.png
[7,7] = [7,4,1+]
(*772)
CDel node c1.pngCDel split1-77.pngCDel nodeab c2.png = CDel node c1.pngCDel 7.pngCDel node c2.pngCDel 4.pngCDel node h0.png
Symbol t{7,4} tr{7,7}
Coxeter diagram CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node.png CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 7.pngCDel node 1.png

Symmetry

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.

Small index subgroups of [7,7]
Type Reflectional Rotational
Index 1 2
Diagram 772 symmetry 000.png 772 symmetry aaa.png
Coxeter
(orbifold)
[7,7] = CDel node c1.pngCDel 7.pngCDel node c1.pngCDel 7.pngCDel node c1.png
(*772)
[7,7]+ = CDel node h2.pngCDel 7.pngCDel node h2.pngCDel 7.pngCDel node h2.png
(772)

Related polyhedra and tiling

References

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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.

See also

External links


  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

Truncated_order-4_heptagonal_tiling
 



 



 
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