  We consider a Bianchi type III axisymmetric geometry in the presence of an
electromagnetic field. A first result at the classical level is that the
symmetry of the geometry need not be applied on the electromagnetic tensor
$F_{\mu\nu}$; the algebraic restrictions, implied by the Einstein field
equations to the stress energy tensor $T_{\mu\nu}$, suffice to reduce the
general $F_{\mu\nu}$ to the appropriate form. The classical solution thus found
contains a time dependent electric and a constant magnetic charge. The solution
is also reachable from the corresponding mini-superspace action, which is
strikingly similar to the Reissner-Nordstr{\"o}m one. This points to a
connection between the black hole geometry and the cosmological solution here
found, which is the analog of the known correlation between the Schwarzschild
and the Kantowski-Sachs metrics. The configuration space is drastically
modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave
geometry. We map the emerging linear and quadratic classical integrals of
motion, to quantum observables. Along with the Wheeler-DeWitt equation these
observables provide unique, up to constants, wave functions. The employment of
a Bohmian interpretation of these quantum states results in deterministic
(semi-classical) geometries most of which are singularity free.
