Challenge

Build Space-filling Polyhedra

Photo of an autonomous robot building a structure using a geometric building block.
SOLL-E a robot for building structures carries a polyhedral building block at NASA's Ames Research Center in Silicon Valley, California. Image from NASA/Dominic Hart

Build polyhedral models that fill 3D space with no gaps or overlaps.

  • What polyhedra are space filling by themselves? What about combinations of multiple polyhedra?
  • What are zonohedra, stereohedra, parallelohedra, and plesiohedra? How are they related? What is centrally symmetry?
  • Who is Evgraf Fedorov? What are Space Groups and Wallpaper Groups?
  • How do different space filling structural designs differ in density, stiffness, and other physical properties?
  • What are examples of natural and man-made space filling structures at different physical scales from nanostructures to large scale architecture?

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