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. . . .

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?

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

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of. . . .

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?

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. . . .

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

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