In practice, two kinds of halfway-models have been used, shown in Fig. 1. The first, used by Shapiro and by Phillips (see Fig. 2, left), is a Boy's surface, which is an immersed projective plane. In other words it is a way of immersing a sphere in space such that antipodal points always map to the same place. Thus there are two opposite sheets of surface just on top of each other. If we can succeed in pulling these sheets apart and simplifying the surface to a round sphere right-side-out, then pulling them apart the other way will lead to the inside-out sphere.