Exploring The Platonic Solids Through Construction

    The pattern that is shown below is called a NET.  Nets are 2-d representations of 3-d objects. (with a little manipulation that is.)  GSP can be used to create these nets so that you may construct models of the Platonic solids we have discussed in previous lessons.  The links below will give you Nets for a Tetrahedron, and an icosohedron.  Print these out for use later in the period.  Then use GSP to create nets for:
  1. A Hexahedron

  3. An Octahedron

  5. A Dodecahedron

Tetrahedron Net
Icosohedron Net

    Keep in mind when making your own nets, that there are certain ways you must put the polygons together to yield the correct results.  Below is an example of a net designed to fold into a Hexahedron.  Do you think it is a valid design?

    Notice right away that there are seven faces when a Hexahedron has only six faces.  This is not a net that will yield a Hexahedron!