In an earlier post (“Morphing the tiling of octagons and squares – a new twist“) I have varied the angles between the lines of the tiling and their generating grid lines. This gave us new tilings without mirror symmetry. I now consider the tiling of dodecagons and triangles. This gives us similar results. The resulting quasiperiodic tilings again are not mirror symmetric.
Here is the quasiperiodic tiling with big hexagons:
At the upper left we see a nice twirling shape with 12-fold rotational symmetry. Its mirror-image cannot be found in this tiling. Further twisting we get a tiling with stars:
This tiling appears to have even more rotating dynamics. But seen from further away, all these tilings look quite similar.