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Figure 8
A list of all possible tiles (with respect to their orientations and placement of a shallow hole) in rhombic Penrose tilings and their duals in [{\cal S}^{\perp}]. Tiles are depicted relative to the shallow hole. The exact correspondence between a tile in the list and a projection of a 2-boundary is, for example, the following. If a tile of type R1 corresponds to [\pi_{\parallel}(P(-+\bigcirc\bigcirc+))], the dual triangle R*1 is equal to [\pi_{\perp}(P^{*}(-+\bigcirc\bigcirc+)) + \pi_{\perp}({\bf a}_{ 1})], i.e. we capture its actual position in ⊥-space. Fixing the positions of the duals allows us to work in coordinates relative to a given point, the `origin'. Everything is then shifted by a suitable vector representing the relative distances of objects from the origin.

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ISSN: 2053-2733
Volume 79| Part 5| September 2023| Pages 399-411
https://doi.org/10.1107/S2053273323004990
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