Robotic construction systems often treat the material system and the robot as separate design problems, locating intelligence primarily in hardware, sensing, motion planning, and control. This project instead investigates how geometric intelligence can be encoded within architected material systems to simultaneously address requirements for robotic grasping, self-alignment, reversible connection, structural performance, and three-dimensional aggregation. We introduce a self-aligning compound nested lattice module composed of conjoined cuboctahedral-octahedral units. The cuboctahedral features of the modules provide defined surfaces for robotic grasping and alignment, while the octahedral features incorporate screw-releasable snap-fit connectors and corresponding receptors. Additionally, we present a nested arrangement that enables interlocking aggregation along the x, y, and z axes. We demonstrate the system through furniture and architectural scale structures assembled using both a robotic arm and mobile assembler. The resulting configurations include seating, spanning structures, surfaces, and vertical frames. Compression testing of the compound module produced a stiffness of 4,556 N/mm, a maximum load of 3,445 N, and a compressive modulus of 17.5 MPa. The modules can also be disassembled and reused across different configurations, supporting reconfigurable and circular construction.

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