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How do complicated structures self-assemble? How can random processes produce
beautiful, symmetric, and complex designs? How can we build structures that optimally
and completely fill 3D space? In this workshop, we will have you build a variety of
polyhedral using a variety of construction materials and see how mathematical
projections help solve 4D design problems. The fourth dimension in 4D printing is time.
Albrect Dürer, the artist, wrote a manual on the mathematics of perspective for artists in
1525 wherein he introduced what we call Dürer nets which are now widely used in
origami construction of polyhedra. In the 1880’s, the mathematician Schlegel introduced
what we call Schlegel diagrams. Afterwards, Alicia Boole focused on how to visualize
four-dimensional polytopes. In 1954 the nontraditional, surrealist Salvador Dalí used her
mathematical approach to produce his famous oil-on-canvas painting “The Crucifixion
(Corpus Hypercubus).” We will use a variety of materials to construct three dimensional
polyhedra and produce multiple two dimensional geometric and topological projections
of the polyhedral that you have built and to infer some fundamental graph theoretic
relationships about vertices, edges, and faces. From there we will move towards
understanding how viruses self-assemble by exploring the principles of self-assembly,
fab labs, and four-dimensional printing.
