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Euler‐Poincaré characteristic of a randomly filled three‐dimensional network

The random filling of a three‐dimensional face‐centred cubic network is simulated on a computer at increasing densities between 0 and 1. The Euler‐Poincaré characteristic (for the spaces ℝ0, ℝ1, ℝ2 and ℝ3) is then measured on all the simulated structures. A quantitative description of this simple densification process is obtained and the maxima observed correspond to the highest values practically attainable for the stereological parameters.