Three-dimensional distorted black holes

We present three-dimensional, non-axisymmetric distorted black-hole initial data which generalize the axisymmetric, distorted, non-rotating and rotating single black-hole data developed by Bernstein, Brandt and Seidel. These initial data should be useful for studying the dynamics of fully 3D, distorted black holes, such as those created by the spiralling coalescence of two black holes. We describe the mathematical construction of several families of such datasets, and show how to construct numerical solutions. We survey quantities associated with the numerically constructed solutions, such as ADM masses, apparent horizons, measurements of the horizon distortion and the maximum possible radiation loss.