Educação Superior::Ciências Exatas e da Terra::MatemáticaW. Heisenberg's real matrix group provides a noncommutative translation group of an affine three-space. The Nil-geometry, which is one of the eight Thurston three-geometries, can be derived from this group. E. Molnár proved that the homogeneous three-spaces have a unified interpretation in the projective three-sphere PS³(V_4,V^4,R). Here, the tori of the Nil-space are visualized