In geometry, the Hexakis triangular tiling is a tiling of the Euclidean plane. It is an equilateral triangular tiling with each triangle divided into six triangles from the center point. (Alternately it can be seen as a hexagonal tiling divided into twelve triangles.)
It is labeled V4.6.12 because each right triangle face has three types of vertices: one with 4 triangles, one with 6 triangles, and one with 12 triangles. It is the dual tessellation of the great rhombitrihexagonal tiling which has one square and one hexagon and one dodecagon at each vertex.
It is topologically related to a polyhedra sequence. This group is special for having all even number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane.
The hexakis triangular tiling is a useful starting point for making paper models of deltahedra, as each of the equilateral triangles can serve as faces, the edges of which adjoin isosceles triangles that can serve as tabs for gluing the model together.
