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 the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

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

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

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?

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

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

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. . . .

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?