### Take Ten

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3 cube?

### Rhombicubocts

Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?

### Cut Nets

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

# Lighting up Time

##### Stage: 2 and 3 Challenge 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 .