Triheptagonal Tiling
Get Triheptagonal Tiling essential facts below. View Videos or join the Triheptagonal Tiling discussion. Add Triheptagonal Tiling to your PopFlock.com topic list for future reference or share this resource on social media.
Triheptagonal Tiling
Triheptagonal tiling

Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration (3.7)2
Schläfli symbol r{7,3} or ${\displaystyle {\begin{Bmatrix}7\\3\end{Bmatrix}}}$
Wythoff symbol 2 | 7 3
Coxeter diagram or
Symmetry group [7,3], (*732)
Dual Order-7-3 rhombille tiling
Properties Vertex-transitive edge-transitive

In geometry, the triheptagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 heptagonal tiling. There are two triangles and two heptagons alternating on each vertex. It has Schläfli symbol of r{7,3}.

Compare to trihexagonal tiling with vertex configuration 3.6.3.6.

## Images

 Klein disk model of this tiling preserves straight lines, but distorts angles The dual tiling is called an Order-7-3 rhombille tiling, made from rhombic faces, alternating 3 and 7 per vertex.

## 7-3 Rhombille

In geometry, the 7-3 rhombille tiling is a tessellation of identical rhombi on the hyperbolic plane. Sets of three and seven rhombi meet two classes of vertices.

7-3 rhombile tiling in band model

## Related polyhedra and tilings

The triheptagonal tiling can be seen in a sequence of quasiregular polyhedrons and tilings:

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 8 forms.

## 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.