On the geometries of planes and the states of particles

Propositional calculus is used to interpret projective planes as spaces of states. For finite planes the 3 lowest lying octets (baryonic, antibaryonic, mesonic) are fitted, together with 64 standard strong vertices, in the smallest exceptional non-Desarguesian plane. In the infinite case, the lines in a Euclidean plane were redefined and so some spatial symmetry appeared as a broken symmetry. This may be interpreted as a hadronic medium in the sense of Santilli.