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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?

Face Painting

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.


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?

Cut Nets

Age 7 to 11
Challenge Level

Printing out the shapes, cutting them out and folding them up may help. Here is a downloadable word document to help.

The shapes are a cube, cuboid, tetrahedron, square pyramid, pentagonal pyramid, hexagonal pyramid, triangular prism, pentagonal prism, trapezoid prism.