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 ${\displaystyle \left\{\begin{array}{c}7\\ 3\end{array}\right\}}$
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.

7-3 rhombille tiling
Faces	Rhombi
Coxeter diagram
Symmetry group	[7,3], *732
Rotation group	[7,3]+, (732)
Dual polyhedron	Triheptagonal tiling
Face configuration	V3.7.3.7
Properties	edge-transitive face-transitive

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.

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7-3 rhombile tiling in band model

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

Quasiregular tilings: (3.n)2 [v · d · e]
Sym. *n32 [n,3]	Spherical			Euclid.	Compact hyperb.		Paraco.	Noncompact hyperbolic
	*332 [3,3] Td	*432 [4,3] Oh	*532 [5,3] Ih	*632 [6,3] p6m	*732 [7,3]	*832 [8,3]...	*∞32 [∞,3]	[12i,3]	[9i,3]	[6i,3]
Figure
Figure
Vertex	(3.3)2	(3.4)2	(3.5)2	(3.6)2	(3.7)2	(3.8)2	(3.∞)2	(3.12i)2	(3.9i)2	(3.6i)2
Schläfli	r{3,3}	r{3,4}	r{3,5}	r{3,6}	r{3,7}	r{3,8}	r{3,∞}	r{3,12i}	r{3,9i}	r{3,6i}
Coxeter