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Euler Number

Leonhard Euler discovered many things that have to do with polyhedra. His most famous is the Euler Number. Euler noticed that if you add the number of faces and vertices of most solids, and then subtracted the number of edges you would get 2. Faces are the 2-Dimensional figures on the solid figures. For example a cube has 6 square faces. Vertices are where the edges meet, the corners.

Look at the pictures, they might help you fill in the chart. The white balls are representing the vertices. On the chart you should fill in the number of vertices. Then add the faces (already given) and the vertices.

	Number of Faces	Number of Vertices	Sum of the number of Faces and Vertices	Number of Edges
Tetrahedron	4			6
Hexahedron (cube)				12
Octahedron	8			12
Dodecahedron	12	20	32	30
Icosahedron	20	12	32	30

The Euler number has to do with the duals in polyhedra, the hexahedron and the octahedron, and the dodecahedron and the icosahedron. I filled in the dodecahedron and the icosahedron for you. They are an example of duals because the faces of one are equal to the vertices of the other. Also their edges are always the same.

The models above were created with Zometools.