STUDYING THREE-DIMENSIONAL GEOMETRY

After studying two-dimensional geometry for several months the students started their study of 3-D geometry by building polyhedra.

 

As part of our study of geometry students are asked to build 16 different polyhedra.  The students learn that the polygons they studied earlier can now be used to make the faces of different polyhedra.  Using straws students build polyhedra with different qualities, such as a polyhedron with 6 square faces, or a polyhedron with 20 equilateral triangles, or a polyhedron with 12 pentagons, or a polyhedron with 4 equilateral triangles.

After students build the polyhedra they are asked to see if they can find a pattern between the number of faces, edges, and vertices.  Students often find other patterns as they look at the data.  But they also find that the number of edges is always the largest and that by adding the number of faces and vertices and subtracting 2 they get the number of edges.   This is better known as Euler's Formula. 

On the first day of studying circles, we fold a circle into a tetrahedron and a truncated tetrahedron.  After 20 students have completed their truncated tetrahedron the class pools their shapes together to form an icosahedron (a solid made up of 20 triangular faces.)

Rev. 08/26/09