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Figure 4
Relationship between the decorated F-type 3D AKN tiling with edge length of a and that with edge length of τ2a. (a) Acute rhombohedron decorated with two positions that divide the longer body-diagonal by τ:1:τ. (b) Dodecahedral star OD used for the decoration. (c) 6D structure of the decorated F-type 3D AKN tiling with edge length of a, which is obtained by adding dodecahedral star ODs with edge length of a, at bc0 and bc1, to the 6D superstructure in Fig. 3[link](e). The red and blue line segments represent the 2D sections of the dodecahedral star ODs, which generate the two positions represented by the red and blue balls in (a), respectively. (d) 6D structure of the decorated F-type 3D AKN tiling with edge length of τ2a obtained by the similarity transformation of order 2 from (c). The thick black squares in (c), (d) indicate the 2D sections of the 6D unit cell.

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ISSN: 2053-2733
Volume 80| Part 6| November 2024| Pages 422-438
https://doi.org/10.1107/S2053273324008568
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