By embedding symmetry in a 3D microfluidic geometry (e.g., octahedral symmetry shown in the following figure), we realized distinct microfluidic functions classified by subgroups of these symmetries. 

These functions include a strain-free flow in 3D, which can be used for trap-free manipulations of microscale objects, as demonstrated below by entraining particles in a 3D volume (here, 200 μm x  200 μm x 100 μm) to imprint a designated "UCM" pattern.