In 1977 R. Ammann found several sets of aperiodic tiles. This one (his set A5) is certainly the best-known of those. It allows tilings with perfect 8fold symmetry. The substitution factor is $1+\sqrt{2}$ - sometimes called the ‘silver mean’ - which was the first irrational inflation factor known …
With Decoration Finite Rotations Polytopal Windowed Tiling Canonical Substitution Tiling Rhomb Tiles Mld Class Ammann Matching Rules