Nets of solids

The idea

A net is a shape on a flat surface that can be folded into a solid, that is, the solid unfolded onto a plane, without any supporting flaps; a solid can have more than one net.

A box from one flat sheet

A cube-shaped box can be made from one flat sheet of card, folded along lines. The flat shape that folds into the solid is called a net.

How many squares does the flat card for a cube have?

• 4
• 6
• 8

Fold the nets

Pick a flat shape and press Fold it. The dashed lines are the folds. The squares are numbered so you can follow them. Does it close into a cube?

Nets of a cube

A net is a shape on a flat surface that can be folded into a solid, that is, the solid unfolded onto a plane, without any supporting flaps. A solid can have more than one net.

You folded different shapes into the same cube. A cube has 11 different nets in all. But not every shape of 6 squares is one: in some, two squares land on the same face and a face is left open.

Notes

A net is a shape on a flat surface that can be folded into a solid: the solid unfolded onto a plane, with no supporting flaps. A solid can have more than one net.

Check yourself

Which of these flat shapes is a net of a cube?

The net of a box is cut from card with little flaps added, to stick the faces together. What is left out when we talk about the net?

This net is folded into a cube. Which numbered square is opposite square 2?

Answer: 5

In this net the opposite pairs are 1 and 4, 2 and 5, 3 and 6.

Meera says, "A cube has only one net, because a cube is only one shape." Is she right?

• Shape A. In A, two squares are on the same side of the row of four. Both fold over onto the same face.
• Shape B. B has five squares in a row. The fifth square folds round onto the first.
• Shape C — correct. Yes! Fold C and every square lands on its own face.
• The faces of the box. The faces are exactly what the net shows.
• The supporting flaps used for sticking — correct. Yes! The net is only the shape formed by unfolding the solid, not the extra flaps.
• The fold lines. The folds are part of the net: they are where the faces are joined.
• No. A solid can have more than one net: different flat shapes fold into the same cube. — correct. Yes! You folded different nets into the same cube, and a cube has 11 different nets.
• Yes. One solid has exactly one net.. You folded more than one flat shape into a cube.
• No. A cube has no net at all.. A cube can be cut open and laid flat: that flat shape is a net.