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We identify three fundamental properties of lattice robots such as (1) discreteness (2) translational symmetry and (3) composition, and explain the analogy of lattice robots kinematics and crystal symmetry described by space groups. Then we give the possible connectors symmetries and orientations compatible with space groups, and the possible sliding and hinge joints locations and orientations compatible with the displacements in such groups. We present a framework for the design of latticedoi:10.1109/robot.2008.4543748 dblp:conf/icra/BrenerAB08 fatcat:augk3td4zjgtnkvndgyio3wtsi