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Context. Analytical and numerical analysis of the SimpleX radiative transfer algorithm, which features transport on a Delaunay triangulation. Aims. Verify whether the SimpleX radiative transfer algorithm conforms to mathematical expectations, to develop error analysis and present improvements upon earlier versions of the code. Methods. Voronoi-Delaunay tessellation, classical Markov theory. Results. Quantitative description of the error properties of the SimpleX method. Numerical validation ofdoi:10.1051/0004-6361/200913439 fatcat:m2sfy5mswjathes3oquqlujn4m