Family of lines formed with parastichy segments, all rotating with the same orientation, corresponding to the smallest separation given by a Fibonacci number fu with an even u (for conservation of the rotation orientation). The colour code is the same as in Figs. 2 and 3: red for six neighbours, blue for five, green for seven. A new line originates when a new Fibonacci number, with these properties (the smallest with even u), appears in the list of separations with neighbours. Except for very small s, this happens on sites with pentagonal cells. These sites are gathered in one of two rings of pentagonal cells, such that in a heptagon–pentagon dipole the new Fibonacci number is not in the list of separations for the site with the heptagonal cell, but the line is oriented as the dipole. All these lines play the role of reticular lines found in two-dimensional crystals and clearly show the dislocations as an insertion of an extra line.