Eulerian and Hamiltonian Graphs · Superchallenge problem

Six warehouses $0,\ldots,5$ are linked ONLY by roads $14, 04, 35, 23, 12, 01, 25, 05, 34$ (nine roads, every warehouse having exactly $3$ roads). Counting two closed tours as the same when they use the same set of roads, how many distinct Hamiltonian cycles (tours visiting every warehouse exactly once) does this road network have?