Supergravity solutions without triholomorphic U(1) isometries

We investigate the construction of five-dimensional supergravity solutions that do not have any triholomorphic U(1) isometries. We construct a class of solutions that in various limits of parameters reduces to many of previously constructed five-dimensional supergravity solutions based on both hyper-Kaehler base spaces that can be put into a Gibbons-Hawking form and hyper-Kaehler base spaces that cannot be put into a Gibbons-Hawking form. We find a new solution which is over triaxial Bianchi type IX Einstein-hyper-Kaehler base space with no triholomorphic U(1) symmetry. One special case of this solution corresponds to a five-dimensional solution based on Eguchi-Hanson type II geometry.