Twisting the tiling of dodecagons and triangles

Twisting the tessellation of dodecagons and triangles by angles of 15 degrees results in big hexagons.

Using angles of 30 degrees we get a periodic tiling of triangles and stars.

In an earlier post (“Morphing the tiling of octagons and squares ā€“ 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:

Result of doubling the periodic tiling of large hexagons and triangles.

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:

Here I have used the tiling of stars and triangles.

This tiling appears to have even more rotating dynamics. But seen from further away, all these tilings look quite similar.

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