For three of the six regular polytopes in four dimensional space,
the stereographic projection has the geometry of a bubble cluster.
Here we see two projected images of the dodecaplex or 120-cell,
and one of the hypercube or 8-cell. These images are from
my article "Generating and Rendering Four-Dimensional Polytopes",
I have also written a java applet to illustrate the same kind of
down one dimension, where regular polyhdra project to planar