A enneagonal tiling of the plane is proposed. A self-sirnilar pattern is obtained by using eight basic shapes. This pattern presents rotational symmetry and no translational invariance. ' ) C.P. 702, CEP 30.161-970. Belo Horizontc, Brazil. ') CEP 36.570.000, ViGosa (MG). Brazil.

Since the experiment of Shechtman et al. [l], which shows the existence of a system with icosahedral symmetry, quasiperiodic systems have been intensively investigated. One of the quasiperiodic lattices is the so-called second-order Fibonacci chain [2], which can be seen as the projection along the icosahedral direction of a three-dimensional pattern with fivefold symmetry [3]. The third-order Fibonacci chain was considered recently by Terauchi et al. [4] who studied the diffraction pattern of this lattice grown by molecular beam epitaxy (MBE) of semiconducting layers A = AlAs, B = A1,,,Ga,,,As, and C = GaAs. Another work that used a third-order Fibonacci sequence was recently made [5]. In [5], hereafter named TI (Tiling I), we proposed a heptagonal quasiperiodic tiling of the plane associated to the third-order Fibonacci sequence S, = 2S,-, + S n -2 -S n -3 . Such tiling presents self-similarity and rotational symmetry but is not translationally invariant.In this note we take a third-order Fibonacci sequence defined as [4] which can be generated by A + B , B + A C , C + C B .The corresponding transformation matrix iswith the secular equation I ) C.P. 702, 30161-970 Belo Horizonte, Brazil. ') 36570-000 ViCosa, Brazil.