Triheptagonal tiling

Triheptagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration(3.7)2
Schläfli symbolr{7,3} or
Wythoff symbol2 | 7 3
Coxeter diagram or
Symmetry group[7,3], (*732)
DualOrder-7-3 rhombille tiling
PropertiesVertex-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


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.

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.


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