3D shapes and their properties

problem
Little boxes

Age

7 to 11

Challenge level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
problem
Face painting

Age

7 to 11

Challenge level

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.
problem
Dodecamagic

Age

7 to 11

Challenge level

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
problem
Child's play

Age

7 to 11

Challenge level

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?
problem
Three cubed

Age

7 to 11

Challenge level

Can you make a 3x3 cube with these shapes made from small cubes?
problem
Sponge sections

Age

7 to 11

Challenge level

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
problem
Cut nets

Age

7 to 11

Challenge level

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
problem
A chain of eight polyhedra

Age

7 to 11

Challenge level

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?
problem
Triangular faces

Age

7 to 11

Challenge level

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
problem
Tetrahedron faces

Age

7 to 11

Challenge level

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?