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Figure 6
Comparison of tilings derived from the vertex set of the chiral spiral cyclic twins with m = 8, 10, 12 (Fig. 5[link], right-hand side from top to bottom) and the corresponding quasicrystal tilings constructed from the same set of tiles (triangles, squares, rhombuses). In particular, the case m = 8 is shown with cyan/magenta tiles (top), the case m = 10 is shown with dark-red/dark-blue tiles (middle) and the case m = 12 is shown with red/green/blue tiles (bottom). The chiral spiral cyclic twin tilings are shown on the left-hand side and the quasicrystal tilings are on the right-hand side. Note that in all cases each pair of tilings of common twin modulus m shares the same tile pattern at its core (highlighted by yellow lines surrounding the tiles). Note also that the quasicrystal tilings shown here are mirror symmetric with two-dimensional point group mmm (with the first letter `m' in italic font type corresponding to the m-fold rotation symmetry, while the following letters `m' in roman font each denote a mirror plane), while the chiral spiral cyclic twin tilings are chiral with the symmetry-reduced two-dimensional point group m.

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ISSN: 2053-2733
Volume 79| Part 6| November 2023| Pages 570-586
https://doi.org/10.1107/S2053273323008276
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