Symmetry and symmetry breaking are essential in biology. Symmetry comes in different forms: rotational symmetry, mirror symmetry and alternating right-left symmetry (for example, gliding reflection symmetry). Especially the transitions between the different symmetry forms are important because they specify crucial points in cell biology, including gastrulation in development, formation of the cleavage furrow in cell division, or the front in cell polarity. However, the mechanisms of these symmetry transitions are not well understood. Here, we have investigated the fundamental properties of symmetry and symmetry transitions of the cytoskeleton during cell movement. Our data show that the dynamic shape changes of amoeboid cells are far from random, but are the consequence of refined symmetries and symmetry changes that are orchestrated by small G-proteins and the cytoskeleton, with local stimulation by F-actin and Scar, and local inhibition by IQGAP2 and myosin.