  We complete the TOP classification of 2-knots with torsion-free, solvable
knot group by showing that fibred 2-knots with closed fibre the Hantzsche-Wendt
flat 3-manifold $HW$ are not reflexive, while every fibred 2-knot with closed
fibre a $\mathbb{N}il^3$-manifold with base orbifold $S^2(3,3,3)$ is reflexive,
and by giving explicit normal forms for the strict weight orbits of normal
generators for the groups of all knots in either class. We also determine when
the knots are amphicheiral or invertible, and show that the only non-trivial
doubly null-concordant knots with such groups are those with group
$\pi\tau_29_{46}$.
