  Systems of dyadic cubes are the basic tools of harmonic analysis and
geometry, and this notion had been extended to general metric spaces. In this
paper, we construct systems of dyadic cubes of complete, doubling, uniformly
perfect metric spaces, such that for any two points in the metric space, there
exists a chain of three cubes whose diameters are comparable to the distance of
the points. We also give an application of our construction to previous
research of potential analysis and geometry of metric spaces.
