Challenge

Build Deltahedra

Black and white photo of chemist Joyce Jacobson Kaufman holding up and focussing carefully on a deltahedral model of a molecule made using a construction kit.
American chemist Joyce Jacobson Kaufman shown using a deltahedral model made using a construction kit in 1964. From the Smithsonian National Postal Museum

Build polyhedra where every face is an equilateral triangle.

  • How many strictly convex deltahedra are there? How can you prove that?
  • How many ways can you connect 2, 3, 4, and 5 tetrahedra?
  • What is the simplest chiral polyhedron?
  • How many 10-faced deltahedra are there? How many with 7 vertices?
  • What is a net? What other ways can you depict deltahedra in 2 dimensions?
  • What is a Boerdijk–Coxeter Helix? What symmetries does it have?
  • How could you write and test instructions for building a specific deltahedron?

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