Axiomatizations of Euclidean geometry in terms of points,equilateral triangles or squares, and incidence

Dimension-free Euclidean geometry over Euclidean ordered fields can be axiomatized in a two-sortedfirst-order language, with points and regular n-gons (with n = 3 or 4) as variables, and with a binary predicate standing for the incidence of a point and a regular n-gon as the only primitive notions.