If we use n=3 in “Dualization method for ten-fold rotational symmetry – the code” we get the well-known periodic tiling with rhombs of 60 degree acute angle and hexagonal symmetry. It is useful for isometric projections, see the geometricon.wordpress.com blog for nice examples. Putting n=6 “doubles” it and gives a quasiperiodic tiling with 12-fold rotational symmetry. If we see only a small part it looks rather chaotic and we have to draw it large-scale to recognize its quasiperiodicity:
Tiling with 12-fold rotational symmetry from the dualization method and 6 sets of parallel lines.
Points given by the projection method and six sets of parallel lines. The green frame shows the space occupied by the above image.
The point of perfect 12-fold rotational symmetry lies at the upper right and we just have enough space to see a few other patterns of local 12-fold rotational symmetry with stars of 12 rhombs. The points resulting from the projection method, see the image at the left and “12-fold rotational symmetry from projection“, shows us where the stars of twelve rhombs are at a very large scale. It seems that local 12-fold rotational symmetry is limited in range and does not extend farther than half the distance between the stars of rhombs.
