So the square perceived the sphere to be an infinite collection of circles pieced together. A second way to view three dimensional polytopes in two dimensions is by means of a projection. Projection is a popular method for Cartographers to create maps of the world from a globe. For instance the United Nations flag is created by a projection of the globe about the south pole. One especially useful type of projection in mathematics is called stereographic projection.
Stereographic projection takes a sphere and maps it over the entire plane in the following manner.
Any other point on the sphere is sent to the unique point on the plane found by intersecting the plane with a line made from the point at the north pole and the point on the sphere. The following picture is an example of a cube which is contained in the sphere, stereographically projected onto the plane. Since polyhedra have as faces regular polygons, one could cut a polyhedra on the edges and fold it in a way so that all the faces are lying on the plane. But before showing these different ways of viewing polytopes, an explanation of how these polytopes are constructed is in order. As regular polyhedra are constructed from regular polygons, so are regular 4-dimensional polytopes constructed from regular polyhedra.