Lesson Three — Deriving Euler’s Formula
From: www.PlatonicSolids.info
Prep
 Create a handout with a grid like the following:
Shape Name

Edges

Vertices

Faces

tetrahedron




octahedron




icosahedron




cube




dodecahedron




 Create a postersized version of the same grid.
Procedure
 Pass out the shapes the students created in the previous
lesson.
 Have students work in small groups counting edges,
vertices, and faces and filling out their grids.
 When the groups have finished counting, create a class
consensus of the counts and fill out the postersized grid.
 Ask students to try to find a pattern that holds for all
of the shapes. You can model this by trying out a relationship such as
Faces + Edges – Vertices.
 Hopefully they will discover some variation on Euler’s
formula: V + F – E = 2. If students come up with different variations,
discuss whether they are equivalent.