Truncated hexagonal tiling

As the name implies this tiling is constructed by a truncation operation applied to a hexagonal tiling, leaving dodecagons in place of the original hexagons, and new triangles at the original vertex locations.

This tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (3.2n.2n), and [n,3] Coxeter group symmetry.

Two 2-uniform tilings are related by dissected the dodecagons into a central hexagonal and 6 surrounding triangles and squares.

Conway calls it a kisdeltille,[4] constructed as a kis operation applied to a triangular tiling (deltille).

[5] It is the dual tessellation of the truncated hexagonal tiling which has one triangle and two dodecagons at each vertex.

A truncated hexagonal tiling can be contracted in one dimension, reducing dodecagons into decagons. Contracting in second direction reduces decagons into octagons. Contracting a third time make the trihexagonal tiling .
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