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.

This entry was posted in Tilings and tagged , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s