Geodesic
A three-dimensional manifold defined by a 4-colored graph which is two-fold covering the 4-colored octahedron graph
Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 2, pp. 37-43.

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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.
Keywords: low-dimensional topology, 3-dimensional manifolds, links, 4-colored graphs, closed braids, spines. 
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M. A. Ovchinnikov. A three-dimensional manifold defined by a 4-colored graph which is  two-fold covering  the 4-colored octahedron graph. Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 2, pp. 37-43. http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_2_a3/

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