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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

Make a ball from triangles!

Face Painting

Age 7 to 11 Challenge Level:

Why do this problem?

This problem is a good way to explore properties of the Platonic solids and gives children opportunities to visualise 3D shapes.

Possible approach

You might like to get children making their own Platonic solids using sheets of paper before trying this activity. This article shows you how to go about it.

Alternatively (or in addition) it would be useful to have some Polydron available for children to build their own solids as they work.

You could introduce the problem by asking children to visualise the cube, asking for justifications of the minimum number of colours needed before they are able to physically make it to check.

Key questions

How many faces/edges/vertices does this shape have?
How many other faces does each face touch?