Semiregular tessellation of squares and triangles. The yellow lines show its generating grid.

This is rather for the completeness sake: The last semiregular tessellation I have not yet used to get a quasiperiodic tiling. It has squares and triangles, as has another tessellation with four-fold rotational symmetry, see “Doubling the tessellation of squares and triangles“. But the triangles are now put together in stripes. Thus this tessellation has only two-fold rotational symmetry. You can see it together with its generating grid in the figure at the left. The periodic lengths of the grid in x- and y-direction have an irrational ratio. Thus we get a quasiperiodic tiling if we superpose two such grids rotated by an angle of 90 degrees. It has four-fold rotational symmetry and a rather chaotic look:

Quasiperiodic tiling of four-fold rotational symmetry.

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