A three-dimensional manifold defined by a 4-colored graph which is two-fold covering the 4-colored octahedron graph

In the theory of three-dimensional manifolds regular graphs of degree 4 with edges colored by 4 colors is a way to represent 3-manifolds. The manifold defined by some certain symmetric 4-colored graph with 12 vertices is recognized in the work. It is shown that the manifold is homeomorphic to the complement space to the link in 3-sphere consisting of the Borromean link and a standard circle which is the 3-order rotation axis of the Borromean link. Some other natural presentations of the manifold are found. It is shown also that the 4-colored graph is the two-fold covering of the 4-colored octahedron graph.