Minimal pseudo-triangulation of the Hopf map and its uniqueness

The Hopf map is a continuous map from the 3-sphere to the 2-sphere, exhibiting a many-to-one relationship, where each unique point on the 2-sphere originates from a distinct great circle on the 3-sphere. This mapping is instrumental in generating the third homotopy group of the 2-sphere. In this paper, we present a minimal pseudo-triangulation of the Hopf map and establish its uniqueness. Additionally, we demonstrate that the pseudo-triangulation corresponding to the 3-sphere is susceptible to a 4-coloring.