Kisrhombille tiling

The kisrhombille tiling is an isohedral tiling with scalene triangles for faces, joining 4, 6, or 12 to a vertex. It is the dual of the uniform great rhombitrihexagonal tiling.

Each face of this tiling is a right triangle. If the shortest edges have length 1, the medium edges have length $$\sqrt2 ≈ 1.41421$$ and the longest edges have length $$\sqrt3 ≈ 1.73205$$. These triangles have angles measuring 30°, 60°, and 90°.