Shape 

Copyright David & Cynthia Thomas, 2009

 

Visualizing 3-Dimensional Objects--Directed Activity: Geometric Solids and Euler's Formula

                                          

Focus

Euler’s Formula

Technologies

·        Platonic Solids model(See Figure 6.6) at the National Library of Virtual Manipulatives (NLVM) website

·        Paper Models of Polyhedra website.

Background

Mathematician Leonhard Euler discovered a formula relating the number of faces (f), edges (e), and vertices (v) of any polyhedron.  To mark a face, edge, or vertex in the NLVM model, click on the object while holding down the Shift key. 

Figure 6.6: NLVM Platonic Solids Model

Tasks

·        Using the NLVM applet, record the number of faces (f), edges (e), and vertices (v) for each shape.  Find a relationship between these variables. 

·        Verify that your formula is also true for all of the Archimedean Solids. 

·        How are the Archimedean Solids different from the Platonic Solids?

·        Using the 2-dimensional nets provided at the Paper Models of Polyhedra website, construct models of two Archimedean Solids and two Platonic Solids.