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Eukaryotic flagella (synonymous with cilia) rely on a microtubule-based axoneme, together with accessory filaments to carryout motility and signaling functions. While axoneme structures are well characterized, 3D ultrastructure of accessory filaments and their axoneme interface are mostly unknown, presenting a critical gap in understanding structural foundations of eukaryotic flagella. In the flagellum of the protozoan parasite Trypanosoma brucei (T. brucei), the axoneme is accompanied by a paraflagellar rod (PFR) that supports non-planar motility and signaling necessary for disease transmission and pathogenesis. Here, we employed cryogenic electron tomography (cryoET) with sub-tomographic averaging, to obtain structures of the PFR, PFR-axoneme connectors (PACs), and the axonemal central pair complex (CPC). The structures resolve how the 8 nm repeat of the axonemal tubulin dimer interfaces with the 54 nm repeat of the PFR, which consist of proximal, intermediate, and distal zones. In the distal zone, stacked "density scissors" connect with one another to form a "scissors stack network (SSN)" plane oriented 45° to the axoneme axis; and ~370 parallel SSN planes are connected by helix-rich wires into a paracrystalline array with ~90% empty space. Connections from these wires to the intermediate zone, then to overlapping layers of the proximal zone and to the PACs, and ultimately to the CPC, point to a contiguous pathway for signal transmission. Together, our findings provide insights into flagellum-driven, non-planar helical motility of T. brucei and have broad implications ranging from cell motility and tensegrity in biology, to engineering principles in bionics.