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 image vertices, not isomorphic to pseudo double wheels, can be transformed into each other, through only tight quadrangulations, by at most image rhombus rotations. If we restrict quadrangulations to be 3-connected, then the number of rhombus rotations can be decreased to image.