Trihexagonal tiling

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Trihexagonal tiling
Trihexagonal tiling
Type Uniform tiling
Vertex figure 3.6.3.6
Schläfli symbol \begin{Bmatrix} 6 \\ 3 \end{Bmatrix}
Wythoff symbol 2 | 6 3
3 3 | 3
Coxeter-Dynkin Image:CDW_dot.pngImage:CDW_6.pngImage:CDW_ring.pngImage:CDW_3.pngImage:CDW_dot.png
Image:CDW_ring.pngImage:CDW_3.pngImage:CDW_ring.pngImage:CDW_3.pngImage:CDW_dot.pngImage:CDW_3.png
Symmetry p6m
Dual Quasiregular rhombic tiling
Properties Vertex-transitive
Trihexagonal tiling
3.6.3.6
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In geometry, the trihexagonal tiling is a semiregular tiling of the Euclidean plane. There are two triangles and two hexagons alternating on each vertex. It has Schläfli symbol of t1{6,3}.

Conway calls it a hexadeltille.

There are 3 regular and 8 semiregular tilings in the plane.

There are two distinct uniform colorings of a trihexagonal tiling. (Naming the colors by indices on the 4 faces around a vertex (3.6.3.6): 1212, 1232.)

[edit] Related polyhedra and tilings

This tiling is topologically related as a part of sequence of rectified polyhedra with vertex figure (3.n.3.n). In this sequence, the edges project into great circles of a sphere on the polyhedra and infinite lines in the planar tiling.


(3.3.3.3)

(3.4.3.4)

(3.5.3.5)

(3.6.3.6)

(3.7.3.7)

(3.8.3.8)

And 3-colors with even orders: 3.2n.3.2n:


(3.4.3.4)

(3.6.3.6)

(3.8.3.8)

[edit] See also

[edit] References

  • Grünbaum, Branko ; and Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman. ISBN 0-716-71193-1.  (Chapter 2.1: Regular and uniform tilings, p.58-65)
  • Williams, Robert The Geometrical Foundation of Natural Structure: A Source Book of Design New York: Dover, 1979. p38
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