A number of interesting graphs are associated with the work of van Cleemput and Zamfirescu (2018).
Two 13- and 15-node graphs, denoted and respectively, were used in the construction of an untraceable quintic polyhedral graph on 108 nodes which is the smallest known such graph.
The 39-node van Cleemput-Zamfirescu graph is the smallest known (and conjectured to be smallest possible) polyhedral quartic nonhamiltonian graph. (It is however traceable.) The 78-node and 108-node van Cleemput-Zamfirescu graphs are the smallest known quartic and quintic graphs, respectively, that are untraceable and polyhedral.
These graphs are will be implemented in the Wolfram Language as GraphData["VanCleemputZamfirescuGraphNNN"].