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The twin-cone beam geometry has been used to reconstruct a three-dimensional object from projections. The reconstruction has been performed by means of the additive algebraic reconstruction technique (ART) extended to three dimensions. Several simulation experiments have been undertaken to explore the effect of pseudo-projections, analytic projections, iteration-dependent damping and interpolation schemes on the performance of the reconstruction. The results indicate that the ART-reconstruction from twin-cone beam projections can be achieved without blurring artefacts. The measured reconstruction error is of the same order of magnitude as the error of a ART-multislice reconstruction from coaxial projections.