Elementary modes (A) and minimal generating set (B) for the example model displayed in Fig. 1 with J2, J3, and J4 as reversible, and J1, J5, and J6 as irreversible reactions. The modes EM1 and GM1 are reversible; thus, the wedge is open in the positive and the negative J4 directions. The reversible cycles do not operate by themselves; they must be coupled to an input output mode. This leads to two additional inequalities (see text). The resulting flux-cone is pointed, revealing a pyramidal shape (C).