Based on the group theory and group algebraic structure of the displacement set, an interesting playing toy of the magic folding square block belonging to one class of single-loop spatial eight-revolute mechanism is offered to illustrate the discontinuous mobility of mechanism. This folding toy’s mobility generally has two finite global dofs as a whole kinematic chain. Nevertheless, during the movement, the permanent finite mobility of mechanism depends on the various positions of joints. When the block profile-shape constraints are taken into account, one bifurcation between one 2-dimensional manifold and one 1-dimensional manifold occurs at an initial transition position and the other bifurcation between two 1-dimensional manifolds exists in another specified configuration. In addition, any motion of one working mode destroys the geometrical condition that is required for the other modes but a bifurcation toward a spatial mode with two finite dofs remains possible by ingoring the profile shape constraints. In fact, there is a discontinuous mobility with a trifurcation among three subsets. It is composed of a general spatial mode with 2-dimensional manifold, one part mobility chain of 2-dimensional manifold and another part mobility chain of 1-dimensional manifold.

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