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Figure 5
(a) Crystallographic description of the Dürer tiling. This very specific structure occurs almost perfectly as planar stacks of the Fe Wyckoff positions in the FeAl3 phase as identified by Black (1955aBB3,bBB4). It has been studied in detail by Ellner & Burkhardt (1993BB11) and Ellner (1995BB10) and has been taken as a basic example in the interpretation of twinning in icosahedral to cubic phase transformations in the (Al, Cu, Fe) system (Bendersky et al., 1989BB2; Bendersky & Cahn, 2006BB1). (b) The Dürer structure can also be analysed as part of the [{\bb Z}^5]-module built with the five vectors that relate the centre Ω to the five vertices of the elementary regular pentagon seen on the left. This periodic subset of the [{\bb Z}^5]-module has unit cell [A = (0,\overline{1},0,0,1)] and [B = (2,1,\overline{2},\overline{2},1)] and two Wyckoff positions w1 = (0,1,0,0,0,) and w2 = (0,0,1,0,0).

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ISSN: 2053-2733
Volume 72| Part 1| January 2016| Pages 55-61
doi:10.1107/S2053273315018197
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