We present an experimental investigation of the collective rearrangement of a hexagonally ordered ﬁlament bundle as a function of twist angle. This study is motivated by the fact that although the twisted filaments represent an architecture widely encountered in biological systems such as bacterial flagella, collagen, fibrin, etc., or in artificial materials such as carbon nanotube ropes, textile yarns, the organization and packing of constituent quasi one dimensional ﬁlaments in twisted bundles is still an unknown problem. We use x-ray computed tomography to reconstruct the three-dimensional structure of the packing, and show that under a prescribed twist the core of the packing maintains the hexagonal symmetry while defects are introduced at the boundaries. We demonstrate that the observed structure is consistent with a mapping of the filament positions to disks packed on a dual non-Euclidean surface with a Gaussian curvature which increases with twist. We use this mapping to understand the collective strain and deformation of the packing with the imposed twist.
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