In this paper we propose a general method for creating a new type of hierarchical structures at any level
in both 2D and 3D. A simple rule based on a rotate-and-mirror procedure is introduced to achieve multilevel
hierarchies. These new hierarchical structures have remarkably few degrees of freedom compared
to existing designs by other methods. More importantly, these structures exhibit synchronized motions
during opening or closure, resulting in uniform and easily-controllable deformations. Furthermore, a
simple analytical formula is found which can be used to avoid collision of units of the structure during
the closing process. The novel design concept is verified by mathematical analyses, computational
simulations and physical experiments.