The EDELWEISS collaboration is searching for WIMP dark matter using natural Ge cryogenic detectors. The whole data set of the first phase of the experiment contains a fiducial exposure of 4.8 kg.day on Ge-73, the naturally present (7.8%), high-spin Ge isotope. The sensitivity of the experiment to the spin-dependent WIMP-nucleon interactions is evaluated using the model-independent framework proposed by Tovey et al.
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