Icosahedral quasiperiodic packing of fibres

Methods for constructing icosahedral packing of fibres are reported. Closest packing constructions were realised using straight fibres of circular cross-section and threaded parallel to five- or three-fold icosahedral axes, or both. Their symmetry point group and related 2D tiling as obtained by cut and projection from periodic hyperspace, are presented in the case of the closest packing of fibres only parallel to the six five-fold axes. As a result of the analysis of the related 2D tiling, constructions can also be made using simple 2D building rules. Future experiments on elasticity properties of composite materials with a quasiperiodic fibrous reinforcement are discussed.