Lesson Four — Generalizing Euler’s Formula

From: www.PlatonicSolids.info

 

 

Prep

• Create a handout with a grid like the following:

 

Shape Name	Vertices (V)	Faces (F)	Edges (E)	V + F – E

 

• Create a poster-sized version of the same grid.
• Prepare an assortment of triangle, square, pentagon, and hexagon shapes.

 

Procedure

• Give each student a new grid.
• Give students access to a variety of shapes.
• Ask students to make up their own polyhedra.  They can use whatever combination of face shapes they want and they should make up names for their new polyhedra.
• Have students count vertices, faces, and edges for their new polyhedra and fill in the chart.
• If all goes well, the last column will have all twos for entries.
• Have students transfer their data to the poster.
• Discuss what this means about Euler’s formula for polyhedra.