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Figure 17
Interesting specific cases appear for the CrB-type structure where ρ = 1 if α = [\pi/K], [K \in {\bb Z}^+]. On top, the case K = 8 generates octagonal twins that are described using a [{\bb Z}]-module of rank 4 defined by the four vectors 1, 2, 3 and 4 in the very same way as the pentagonal module (K = 10) of NiZr. The case of K = 12 leading to dodecagonal twins is also very simple to handle since the corresponding [{\bb Z}]-module is also of rank 4. Unit cells are: octagonal A = [({\overline 1},{\overline 1},1,1)], B = (1,3,3,1); dodecagonal A = [({\overline 1},{\overline 1},0,1)], B = [({\overline 1},1,4,3)] [see Hornfeck et al. (2014BB8) Fig. 7 for an illustration of chiral twins of the CrB type with octagonal and dodecagonal symmetry].

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ISSN: 2053-2733
Volume 74| Part 6| November 2018| Pages 647-658
https://doi.org/10.1107/S2053273318011439
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