Polygons and PolyhedraPolyhedra
Up to now we have just looked at what we can do with polygons in a flat, two-dimensional world. A
Polyhedra cannot contain curved surfaces – spheres and cylinders, for example, are not polyhedra.
The polygons that make up a polyhedron are called its
Polyhedra come in many different shapes and sizes – from simple cubes or pyramids with just a few faces, to complex objects like the star above, which has 60 triangular faces. It turns out, however, that all polyhedra have one important property in common:
Euler’s Polyhedron Formula
In every polyhedron, the number of faces (F) plus the number of vertices (V) is two more than the number of edges (E). In other words,
For example, if a polyhedron has 12 faces and 18 vertices, we know that it must have
This equation was discovered by the famous Swiss mathematician
If you try different polyhedra, like the ones above, you’ll find that Euler’s formula always works. In a later course you’ll learn how to actually prove it mathematically.