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 anglesThe 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.
See also
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-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
External links
Hyperbolic and Spherical Tiling Gallery KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings Hyperbolic Planar Tessellations, Don Hatch