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We propose and investigate a system in which teams of quadrotor helicopters assemble 2.5-D structures from simple structural nodes and members equipped with magnets. The structures, called Special Cubic Structures (SCS), are a class of 2.5-D truss-like structures free of overhangs and holes. Grippers attached to the bottom of each quadrotor enable them to pick up, transport, and assemble the structural elements. The design of the nodes and members imposes constraints on assembly which are incorporated into the design of the algorithms used for assembly. We show that any SCS can be built using only the feasible assembly modes for individual structural elements and present simulation and experimental results with a team of quadrotors performing automated assembly. The paper includes a theoretical analysis of the SCS construction algorithm, the rationale for the design of the structural nodes, members and quadrotor gripper, a description of the quadrotor control methods for part pickup, transport and assembly, and an empirical analysis of system performance.