# From squares to Platonic Solids

Some questioning as a way to get to Platonic Solids:

• What is special about a cube? (compared to a cuboid)
• What is special about squares? (the sides on a square)
• What do we call 2D shapes where all the sides are the same?
• So, can we generalise, what is special about a cube?
• What other regular 2D shapes do you know. Draw them now.
• What other 3D shapes can you picture that can be constructed only with regular 2D shapes? These are called Platonic Solids.

Have a go.  See if you can find some dusty old 2 shapes in a cupboard somewhere.

These are quite cheap or you could make your own from card using this template.

So, here they are in all their glory. The wikipedia page has some nice animations.

The Greeks discovered these 5 and mathematicians since have proved that there are definitely no more, whichever polygons we use.

Next you could complete this table.

Once you have done that, can you spot any patterns in a relationship between F, E and V?  You might even discover Euler’s formula, which holds true for any convex polyhedra, not just the platonic solids.

## V – E + F = 2

Or use (a lot!) of 2d shapes to make nets of these shapes.