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Figure 1
(a) The `hat tile', H (red), superimposed over the vertex-3-transitive hexagonal structure and its mirror image, [\bar H] (blue). The crystallographically distinct vertices 1, 2 and 3 are indicated. The hexagon edge length, u, is the unit distance. (b) A partially filled section of the aperiodic monohedral tiling superimposed over the hexagonal mta net. The nominal unit cell and edge vectors a and b are indicated. Filled circles are the vertices delineating the tiling; the open circles inside the tiles are excluded from the structure. There are significantly more H tiles (red) than [\bar H] tiles (blue). (c) The net mta as a periodic `kite' tiling (Laves [3.4.6.4] tiles); vertices are white in this drawing (from the RCSR database; rotated 30°). (d) The set of 13 [\{ {\bf r}_s\}] vectors describing the locations of the set of 13 vertices (black circles) relative to the center of a hexagon. Vertex types, 1, 2, 3, are indicated. The vector for the center vertex itself is the null vector with zero magnitude, so only 12 arrows are visible.

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ISSN: 2053-2733
Volume 80| Part 1| January 2024| Pages 72-78
https://doi.org/10.1107/S2053273323009506
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