We investigate the construction of five-dimensional supergravity solutionsthat don't have any tri-holomorphic U(1) isometries. We construct a class ofsolutions that in various limits of parameters reduces to many of previouslyconstructed five-dimensional supergravity solutions based on both hyper-Kahlerbase spaces that can be put into a Gibbons-Hawking form and hyper-Kahler basespaces that can't be put into a Gibbons-Hawking form. We find a new solutionwhich is over triaxial Bianchi type IX Einstein-hyperkahler base space with notri-holomorphic U(1) symmetry. One special case of this solution corresponds tofive-dimensional solution based on Eguchi-Hanson type II geometry.
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