Graphs $4_n$ that are isometrically embeddable in hypercubes
  A connected 3-valent plane graph, whose faces are $q$- or 6-gons only, is called a {\em graph $q_n$}. We classify all graphs $4_n$, which are isometric subgraphs of a $m$-hypercube $H_m$. 
Michel Deza, Mathieu Dutour-Sikiric and Sergey Shpectorov