Truncated octagonal tiling

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Truncated octagonal tiling
Truncated octagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.16.16
Schläfli symbol t{8,3}
Wythoff symbol 2 3 | 8
Coxeter diagram CDel node 1.pngCDel 8.pngCDel node 1.pngCDel 3.pngCDel node.png
Symmetry group [8,3], (*832)
Dual Order-8 triakis triangular tiling
Properties Vertex-transitive

In geometry, the Truncated octagonal tiling is a semiregular tiling of the hyperbolic plane. There is one triangle and two hexakaidecagons on each vertex, it has Schläfli symbol of t{8,3}.

Dual tiling[edit]

The dual tiling has face configuration V3.16.16.

Ord8 triakis triang til.png

Related polyhedra and tilings[edit]

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 ten hyperbolic uniform tilings that can be based from the regular octagonal 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.

See also[edit]

References[edit]

  • 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 links[edit]