We have 4 "inside" vertices of degree 2 and 4 "outside" vertices of degree 4 each of which form a hamiltonian circuit but we have to visit the vertex p too..where we get stuck. Without loss of generality assume our path begins at i and we go o,n,m,l,q,k and j,if we visit p we have no way to navigate backward and traverse the 4 "outside" vertices. So,no a hamiltonian circuit doesn't exist.
