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Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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Child's Play

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?

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Making Maths: Triangular Ball

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Face Painting

Age 7 to 11 Challenge Level:

Here is a picture of the five Platonic solids:

platonic solids

Imagine you want to make each of the five Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

Can you find the least number of colours for which this is possible for each polyhedron.

How did you go about finding your solutions?

If you'd like to make these solids out of paper, have a look at Ian Short's article.