A tiling based on 7-fold (resp. 14-fold) symmetry [ND96].
The inflation factor is
The three different edge lengths are proportional to
On a first glance, there seems to exist a centre of perfect 14-fold symmetry:
a 14-tipped star in the upper right corner.
But in fact it is only 2-fold symmetric.
The symmetry is broken by the right- and left-handedness of the tiles.
On rings around the 14-tipped star, this manifests in tiles pointing clockwise or counterclockwise, thus breaking the symmetry.
Nischke, K-P and Danzer, L
A construction of inflation rules based on $n$-fold symmetry
Discrete and Computational Geometry 1996, 15,2, pp. 221-236, 96j:52035