Challenge

Build Dual Pairs

Front cover of Lorenz Stöer's 1567 book Geometria Et Perspectiva
Front cover of Lorenz Stöer's 1567 book Geometria Et Perspectiva

Build pairs of shapes where vertices of one correspond to the faces of the other.

  • What are 2D and 3D duals? Are the duals of 3D space filling shapes also space filling?
  • Which shapes are self-duals? Which duals pairs have sides of equal length?
  • Who is Joseph Catalan? How are Catalan Solids and Archimedean Solids related?
  • What is a Dual Graph? What is a Medial Graph? How are these graph transformations useful in practical applications?
  • What other types of duality, dual systems or models exist in science and nature?
  • What is a polytope? How can you depict shapes and their duals in higher dimensions?

For answers, notes, and supporting materials, enter your license code.

Enter Premium License

Pinned images from our dedicated Pinterest board.