Francesco De Comité

Associate Professor in Computer Science
University of Sciences, Lille
Lille, France

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.

All the Edges of all the Archimedean Solids
Digital Print

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.

Exploring the Edges of Polyhedra
14*14*14cm (each object)
3D print

Choosing some subsets of connected vertices from different polyhedra.

All the edges of all the Catalan solids
Digital print

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.