Fig. 1.

Periodic and quasiperiodic arrangement of atoms. a An example of cubic unit cell in which the icosahedron occupies the corner and body-centered positions. Pink balls indicate atoms. b An example of the Tsai-type icosahedral quasicrystal. The fivefold rotational symmetry and the self-similarity may be observed. c Fibonacci sequence and its approximants. Atoms are denoted by circles, and the long and short interatomic segment is denoted by L and S, respectively. The bracket (e.g., LS for 1/1AC and LSL for 2/1AC) denotes the unit cell