Quasiperiodic packings of fibres with icosahedral symmetry

Abstract

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. But for determining unambiguously all the fibre positions it appears that a mathematical construction has to be made from the cut and projection of a five-dimensional space. Through such a method, the volume fraction of fibrous reinforcement in a composite material can be calculated. The related two-dimensional tiling can be proved to be different from a Penrose tiling. Finally, the characteristics of other icosahedral packings where fibres are parallel to threefold axes or to both threefold and fivefold axes are briefly discussed and a few further experiments on their elasticity properties and photonic band-gap structure are suggested.