  We formulate the necessary and sufficient conditions for the existence of a
pair of maximally incompatible two-outcome measurements in a finite dimensional
General Probabilistic Theory. The conditions are on the geometry of the state
space, they require existence of two pairs of parallel exposed faces with
additional condition on their intersections. We introduce the notion of
discrimination measurement and show that the conditions for a pair of
two-outcome measurements to be maximally incompatible are equivalent to
requiring that a (potential, yet non-existing) joint measurement of the
maximally incompatible measurements would have to discriminate affinely
dependent points. We present several examples to demonstrate our results.
