In geometry, the bisected hexagonal tiling is a tiling of the Euclidean plane. It is an equilateral hexagonal tiling with each hexagon divided into 12 triangles from the center point. (Alternately it can be seen as a bisected triangular tiling divided into 6 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 defined by the face configuration V4.6.2n. 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, and continuing into the hyperbolic plane for any n.
With an even number of faces at every vertex, these polyhedra and tilings can be shown by alternating two colors so all adjacent faces have different colors.
Each face on these domains also corresponds to the fundamental domain of a symmetry group with order 2,3,n mirrors at each triangle face vertex.
D6h (*622) full sym.
Oh (*432) full sym.
|Oh (*432)||Ih (*532)|
The bisected hexagonal 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.