A symmetry analysis of mechanisms in rotating rings of tetrahedra

Rotating rings of tetrahedra are well known from recreational mathematics. Rings of N tetrahedra with N even are analyzed by symmetry-adapted versions of classical counting rules of mechanism analysis. For N ≥ 6 a single state of selfstress is found, together with N − 5 symmetry-distinct mechanisms, which include the eponymous rotating mechanism. For N = 4 in a generic configuration, a single mechanism remains together with three states of self-stress, but uniquely in this case the mechanism path passes through a bifurcation at which the number of mechanisms and states of self-stress is raised by one.