  We investigate the 1/8 BPS geometries with SU(2) x U(1) x SO(4) x R symmetry
in IIB supergravity which were classified by Gava et al, (hep-th/0611065). It
is desirable to have a complete set of differential equations imposed on the
controlling functions such that they are not only necessary but also sufficient
to produce supergravity solutions with those symmetries. We work on this issue
and find a new differential equation for the controlling functions. For a
special case, we exhaust all the remaining constraints and show that they
reduce to one Liouville equation. The solutions of this equation produce
geometries which are locally equivalent to the near horizon geometries of
intersecting D3-branes.
