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# Triheptagonal tiling

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 SchlĂ¤fli symbol of r{7,3}.

Compare to trihexagonal tiling with vertex configuration 3.6.3.6.

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.

See also

Wikimedia Commons has media related to Uniform tiling 3-7-3-7.

Trihexagonal tiling - 3.6.3.6 tiling

Rhombille tiling - dual V3.6.3.6 tiling

Tilings of regular polygons

List of uniform tilings

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.

External links

Weisstein, Eric W., "Hyperbolic tiling", MathWorld.

Weisstein, Eric W., "PoincarĂ© hyperbolic disk", MathWorld.

Hyperbolic and Spherical Tiling Gallery

KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings

Hyperbolic Planar Tessellations, Don Hatch

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