You will need the Platonic Solids Nets for this activity. Not provided at this site yet. (Under construction!)

http://illuminations.nctm.org/imath/3-5/GeometricSolids/GeoSolids2.html

- A
**simple closed surface**has exactly one interior. The interior is hollow. It separates space into exactly three sets of points: the interior points, the points on the surface, and the exterior points. - Write examples of simple closed surfaces. __________________________________
- A
**solid**is the**union of a simple closed surface and its interior points**. Name three everyday solids. _______________________________________________________ - A
**polyhedron**is a**simple closed surface made up of polygonal regions**. (Poly means "many" and hedron means "flat surfaces") Each polyhedron has the following four features: base(s), lateral faces, edges, and vertices. These features are used to classify and name the polyhedron. - A polyhedron is called a
**regular polyhedron**if the**faces**of the polyhedron**are congruent regular polygonal regions**, and**if each vertex is the intersection of the same number of edges**. There are exactly five that can be formed! These polyhedra are often called the**Platonic Solids**in honor of the Greek philosopher Plato. - Think of another solid with polygonal faces. Count the faces, vertices, and edges. Does Euler's Formula still hold?

Use your Platonic Solids to fill in the table. Once you are done, look for a relationship between
the number of edges of each prism. Fill in the last column above. Find a relationship between the
**E**dges, **V**ertices, and **F**aces. This relationship is called **Euler's Formula** (pronounced Oiler).

Write your relationship here: ________________________________

Faces | Vertices | Edges | |

Tetrahedron |
4 triangular | ||

Hexahedron
(Cube) |
6 square | ||

Octahedron |
8 triangular | ||

Dodecahedron |
12 pentagonal | ||

Icosahedron |
20 triangular |

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Copyright 1998 by Margo Lynn Mankus