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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

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 - tiling
Rhombille tiling - dual V3.6.3.6 tiling
Tilings of regular polygons
List of uniform tilings


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., "Poincaré hyperbolic disk", MathWorld.
Hyperbolic and Spherical Tiling Gallery
KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
Hyperbolic Planar Tessellations, Don Hatch

Mathematics Encyclopedia

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