Francesco De Comité
Manipulation of digital images, and use of ray-tracing software can help you to concretize mathematical concepts. Either for giving you an idea of how a real object will look (as with my work on playing cards slide-together presented at Bridges 2010), or to represent imaginary landscapes only computers can handle.
Same method used with the Archimedean solids is applied there to their duals. Some constructions look very similar (like kite hexecontahedron and disdyakis triacontahedron, for example), but there are some subtile differences.
Choosing some subsets of connected vertices from different polyhedra.
Consider the set of the vertices of a polyhedron. Connect each of those vertices with all the other ones, coloring those 'edges' according to their length. This can be seen as a way to show quite all the symmetries of those polyhedra at the same time, or as a tool to extract from this set some interesting shapes.