An intermediate stage in Hrushovski’s construction of flat strongly minimal structures in a relational language L produces ?-stable structures of rank ?. We analyze the pregeometries given by forking on the regular type of rank ? in these structures. We show that varying L can affect the (local) isomorphism type of the pregeometry, but not its finite subpregeometries. A sequel will compare these to the pregeometries of the strongly minimal structures.