We study three-dimensional rapidly rotating Bose-Einstein condensates in a theoretical context. The main results are lower and upper bounds on the Gross-Pitaevskii energy of the dilute Bose gas in the Thomas-Fermi limit. Similar results were already obtained for strongly anharmonic external potentials in 2D and homogeneous external potentials in 2D and 3D whereas we present the treatment of partially anisotropic traps in 3D. Furthermore a complete description and illustration of the

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... density in this limit is given. We also supply the source code for the generation of the illustrations.