The box graph is the graph illustrated above in a number of embeddings. It is a cubic Hamiltonian graph on 14 vertices and 21 edges with graph crossing number 2, graph diameter 3, and girth 5. The graph appears in Robertson et al. (2019) in their study of excluded minors in cubic graphs. Robertson et al. (2019) do not state the origin of the name, which may refer to the box-like graph embedding drawn in their Fig. 3.
It is one of the seven 14-vertex cubic graphs attaining the minimum graph transmission among connected cubic graphs on 14 vertices.
The box graph is implemented in the Wolfram Language as GraphData["BoxGraph"].
