The 28,872,973 linear spaces on 12 points are constructed. The parameters of the geometries play an important role. In order to make generation easy, w e construct possible parameter sets for geometries rst (purely algebraically). Afterwards, the corresponding geometries are tried to construct. We de ne line types, point t ypes, point cases and also re ned line types. These are the rst three steps of a general decomposition according to the parameters which we call TDO. The depth of parameter precalculation can be varied, thereby obtaining a handy tool to react in a exible way t o d i e r e n t grades of di culty of the problem.
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