 | Acta Crystallographica Section A Acta Crystallographica Section A FOUNDATIONS AND ADVANCES |
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![[Figure 2]](gau5006fig2mag.jpg)
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Figure 2
(a) Local triangle–square–rhombus tiling within the NGT. It consists of 20 vertices arranged in two rhombuses, five squares and 12 triangles. The orange-marked shield element encloses one rhombus, one square and two triangles with one vertex position inside the shield. A local mode or phason flip might move the inner vertex of the shield to the open red circle positions which does not change the tiling statistics. The sequence of three dodecagons illustrates such phason flips. (b) The unit vector definition in the physical space (left) and the corresponding four-tuple notation for the vertex positions in the shield (right). (c) The unit vectors defined in the internal space and the dodecagonal AD of the NGT. The latter is partitioned into colored areas depending on the local vertex configuration, as indicated just below. The blue area describes vertices within the shield that can undergo short-distance phason flips. The black dots represent 20 vertices of the characteristic dodecagon of (a). (d) The internal space representation of the area that hosts the vertices within the shield element (filled blue parallelograms) inside the AD and their potential flipped positions (empty parallelograms) outside the AD. The red arrows indicate the two possible phason jumps of the short-axis vertex labeled in (b). |
![[Figure 2]](gau5006fig2.jpg)
| FOUNDATIONS ADVANCES |
ISSN: 2053-2733
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