Challenge

Build Tetrahedra

16th century watercolor illustration of a large tetrahedron next to a small bird
16th century watercolor illustration of a large tetrahedron next to a small bird

Build the simplest polyhedron with 4 3-way connectors.

  • What is a simplex? What are the 1, 2, and 3-dimensional simplexes? How can you envisage higher-order simplexes?
  • What symmetries does a tetrahedron have?
  • Who is Leonhard Euler? What did he discover about polyhedra?
  • How many different ways can you extend the tetrahedron? What is Conway's Notation?
  • Where does the tetrahedron show up in nature and in engineering?
  • How many polyhedra can you make with 5, 6, 7, 8 or N vertices?

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