Foaming three-charge black holes

We find a very large set of smooth horizonless geometries that have the same charges and angular momenta as the five-dimensional, maximally spinning, three-charge, supersymmetric black hole (J(2)=Q(3)). Our solutions are constructed using a four-dimensional Gibbons-Hawking base space that has a very large number of two-cycles. The entropy of our solutions is proportional to root Q. In the same class of solutions we also find microstates corresponding to zero-entropy black rings, and these are related to the microstates of the black hole by continuous deformations.