Cones for the Moulton planes

We present a two-parameter family of affinely connected surfaces which admit the cylinder group as a collineation group of their geodesics. The Moulton Planes in the radial model of Betten, the circular cone, as well as the real affine plane, are part of this family. The Moulton Planes occur in this family in the same way as the real affine plane is contained in a family of cones with decreasing steepness.