Robotic self-assembly allows robots to join to form useful, on-demand structures. Unfortunately, the methods employed by most self-assembling robotic swarms compromise this promise of adaptability through their use of fixed docking locations, which impair a swarm's ability to handle imperfections in the structural lattice resulting from load deflection or imperfect robot manufacture; these concerns worsen as swarm size increases. Inspired by the amorphous structures built by cells and social insects, FireAnt3D uses a novel docking mechanism, the 3D continuous dock, to attach to like robots regardless of alignment. FireAnt3D demonstrates the use of the 3D continuous docks, as well as how a robot can use such docks to connect to like robots and locomote over arbitrary 3D arrangements of its peers. The research outlined in this paper presents a profoundly different approach to docking and locomotion during self-assembly and addresses longstanding challenges in the field of robotic self-assembly.