Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the. . . .
In a recent workshop, students made these solids. Can you think of reasons why I might have grouped the solids in the way I have before taking the pictures?
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Can you work out the dimensions of the three cubes?
In this article, we look at solids constructed using symmetries of their faces.