This application is directed to a linkage system which provides continuous rotation to two or more interconnected quadrilaterals. The basic element of the linkage system is a multi-level link which provides firstly, a non-rotatable connection between two sub-links lying in separate parallel planes and secondly, a rotatable connection for a further link lying in another parallel plane between the planes of the sub-links. By various interconnections between link elements, the quadrilaterals the linkage system will form various geometric patterns as the linkage is rotated. As the quadrilaterals lie in different planes, they may be continuously rotated with respect to each other. The linkage system may be used as a toy, a novelty item and as an educational tool.