Abstract
Octagonal quasicrystal tilings belonging to four different local isomorphism (LI) classes are generated by taking the duals of selected quasiperiodic tetragrids. The four classes produced may be divided into two pairs. Either member of each pair may be decomposed (inflated or deflated) to reproduce the other member of the pair, and, of course, itself. One of the members of each pair consists of squares and rhombs, while the other is derived from a singular tetragrid and thus consists of octagons and hexagons as well. Each member of the first pair not only admits a single infinite 8-fold tiling, but also an infinite cartwheel tiling. Each member of the other pair admits two different 8-fold tilings and, in addition, an infinite 4-fold tiling. Contrary to the published square/rhomb LI class of the first pair, the square/rhomb LI class of the second pair is somewhat more complex in that it contains two inequivalent tiles of each type.
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