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Figure 4
Magnified views of fragments of the P, D and G surfaces (see Fig. 3[link]), with three-dimensional Euclidean symmetry operations marked on the surfaces. The arcs AB, BC and CA correspond to the two-dimensional in-surface (non-Euclidean) reflections R2, R1 and R3, respectively, for all three surfaces (see main text). Left: The P surface, with [Im\overline{3}m] symmetry (including isometries that swap sides of the surface; these are coloured differently here for clarity): A, B and C are located at the 12d (site symmetry [\overline{4}m2]), 24h (mm2) and 8c ([\overline{3}m]) sites, respectively; AB and BC lie in orthogonal mirror planes, CA is a twofold axis. Middle: The D surface ([Pn\overline{3}m]): A, B and C are located at the 6d ([\overline{4}2m]), 12f (222) and 4c ([\overline{3}m]) sites, respectively; AB and BC are twofold axes, CA lies in a mirror plane. Right: The G surface ([Ia\overline{3}d]): A and C are located at the 24d and 16a sites, with point-group symmetries [\overline{4}] and [\overline{3}], respectively; B lies on a twofold axis that is normal to the surface.

ISSN: 2053-2733
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