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Tetrahedron Faces

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?

Redblue

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?

Dodecamagic

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?

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?