Truncated heptagonal tiling

Truncated heptagonal tiling
Truncated heptagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.14.14
Schläfli symbol t{7,3}
Wythoff symbol 2 3 | 7
Coxeter diagram CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 3.pngCDel node.png
Symmetry group [7,3], (*732)
Dual Order-7 triakis triangular tiling
Properties Vertex-transitive

In geometry, the truncated heptagonal tiling is a semiregular tiling of the hyperbolic plane. There are one triangle and two tetradecagons on each vertex. It has Schläfli symbol of t{7,3}. The tiling has a vertex configuration of 3.14.14.

Dual tilingEdit

The dual tiling is called an order-7 triakis triangular tiling, seen as an order-7 triangular tiling with each triangle divided into three by a center point.

 

Related polyhedra and tilingsEdit

This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (3.2n.2n), and [n,3] Coxeter group symmetry.

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 eight forms.

See alsoEdit

ReferencesEdit

  • 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.

External linksEdit