Graph Coloring · Hard problem

The Möbius ladder $M_8$ has vertices $1,\ldots,8$ arranged in the cycle $1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}6\text{-}7\text{-}8\text{-}1$, together with the $4$ "diagonal" edges joining each vertex to the one directly opposite: $15,26,37,48$ ($12$ edges in all, every vertex of degree $3$). What is $\chi(M_8)$?