Fig. 2: Covering based on the Lück decagon.

a HAADF-STEM image along the tenfold axis of decagonal Al₇₄Cr₁₅Fe₁₁ with a Lück-decagon covering superposed. b The Lück decagons are shaded blue to clearly show some defective areas (6.1% of the total area) marked in purple. c The action of phason flipping to eliminate the defects (purple area) visible in b. One or two more Lück decagons are generated in the right column with the disappearance of the purple defects in the left column, after the change of few flat hexagonal (H) tiles. d If the centers of the Lück decagons (red dots) are connected by lines a triangle tiling is created, which resembles the Tübingen-triangle tiling (TTT). For the TTT typical decagonal areas are shaded in transparent red. In the ideal TTT the straight lines would not be broken.