Primitive normality and additivity of free projective and strongly flat polygons

We study into monoids $S$ over which the axiomatizable class of all free, projective, or strongly flat $S$-polygons is primitive normal or additive. It is proved that an axiomatizable class of all free, projective, or strongly flat $S$-polygons is primitive normal iff a monoid$S$ primitive normal. Also it is shown that an axiomatizable class of all free, projective, or strongly flat $S$-polygons is not additive for any monoid $S$.