Tight quadrangulations on the sphere

A quadrangulation is a simple graph on the sphere each of whose faces is quadrilateral. A quadrangulation G is said to be tight if each edge of G   is incident to a vertex of degree exactly 3. We prove that any two tight quadrangulations with n⩾11n⩾11 vertices, not isomorphic to pseudo double wheels, can be transformed into each other, through only tight quadrangulations, by at most 83n-763 rhombus rotations. If we restrict quadrangulations to be 3-connected, then the number of rhombus rotations can be decreased to 2n-222n-22.