Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

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?

How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?

In this article, we look at solids constructed using symmetries of their faces.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .

Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices. . . .

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.