This method of viewing higher dimensional objects as well as others is one way people can understand the shape of higher dimensional space. In Flatland , the method in which the sphere showed its form to square was by raising its body through the Flatland surface. The square saw at first a point that quickly grew to a circle, which continued increasing in size, and then started decreasing in size until it became a point, and then it disappeared. 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.