  We present a measurement of the cosmogenic activation in the germanium
cryogenic detectors of the EDELWEISS III direct dark matter search experiment.
The decay rates measured in detectors with different exposures to cosmic rays
above ground are converted into production rates of different isotopes. The
measured production rates in units of nuclei/kg/day are 82 $\pm$ 21 for $^3$H,
2.8 $\pm$ 0.6 for $^{49}$V, 4.6 $\pm$ 0.7 for $^{55}$Fe, and 106 $\pm$ 13 for
$^{65}$Zn. These results are the most accurate for these isotopes. A lower
limit on the production rate of $^{68}$Ge of 74 nuclei/kg/day is also
presented. They are compared to model predictions present in literature and to
estimates calculated with the ACTIVIA code.
