-projections from 3 space

 

Objective::

Students will learn to create straight line planar graphs by projecting polyhedra onto the plane. The figures can be embedded so that all edges are straight and no edges overlap.

Materials :

• Geometer's sketchpad or Cabri geometry software
• ruler
• regular polygedron die
• Handout "Polyhedra Properties, an Investigation"

Lesson:

Begin by having students investigate Euler's formula using the handout. After tehy complete their investigation, have them state Euler's formula.

Using the tetrahedron die, illustrate the figure in the plane. Emphasize the absence of the base and the need to count the plane region outside of the graph as a face. The region outside the graph is separated by a continuous closed curve [Jordan curve} and divides the plane into two regions.

Assignment:

Have students complete the projection of each of the remaining 4 regular polyhedra onto the plane. Emphasize the projection should be embedded, contain only straight lines and no edges should meet in any place other than a vertex of the original polyhedra.

Handouts:

• "Polyhedra Properties, an Investigation" - [email for a copy]