Quasiperiodic packings of fibres with icosahedral symmetry.

Different icosahedral packings of fibres have been experimentally realized. A packing construction with straight fibres of the same circular cross section, only parallel to fivefold icosahedral axes and respecting the closest packing condition, is reported. Its characteristics of point-group symmetry and related two-dimensional tilings are analysed.

Icosahedral quasiperiodic packing of fibres parallel to fivefold and threefold axes.

Building rules are examined for an icosahedral quasiperiodic packing of fibres with axes parallel to the ten threefold axes, first employing an experimental construction and afterwards a mathematical demonstration using the cut-and-project method applied in hyperspace. As a result of this latter approach, very simple two-dimensional (2D) building rules are proposed. Similar simple 2D rules have also been proposed for the case of an icosahedral quasiperiodic packing with fibre axes parallel to the six fivefold axes [Duneau & Audier (1999).