### 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.

### A Mean Tetrahedron

Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?

# Lighting up Time

##### Age 7 to 14Challenge Level

This lampshade was photographed in Rimini in Italy. In Africa candle holders exactly like this are often made from wire.

• Do you know the mathematical name for this shape?
• Can you see lots of triangles?
• What "type" of triangles are they and how many of them were needed to make this lampshade?
• What other shapes can you see?
• Could you make a polyhedron like this from card? How would you do it?

There's another image you might like to take a look at in the Notes .