The faces you cannot see
A cube has 6 faces, and every face is the same square. Look at a cube from one corner, and you can see only 3 of its faces: the top, the front and one side. The other 3 are hidden at the back, on the far side and underneath.
From this corner, 3 of the cube's 6 faces can be seen.
Open it out
Think of the cube as a cardboard box. Cut along some of its edges and fold the faces out until they all lie flat. The flat shape is called a net of the cube. Every square in the net is one face of the cube, so all 6 faces can be seen and counted at once. Fold the net back up along the same edges, and it makes the cube again.
Follow one face as the box opens. The lid is gold. It starts on top of the cube, swings out as the box opens, and ends at the far end of the flat strip.
The same box closed, half open and flat. The gold lid, face 1, stays one face all the way through.
Which faces are opposite
In this net, four squares make a column: the lid, the front, the base and the back. The left and right faces stick out on either side of the base.
Two squares in a straight line with exactly one square between them fold to opposite faces of the cube. The lid and the base have the front between them, so they become the top and the bottom. The front and the back have the base between them. The left and the right faces have the base between them, so they are opposite too.
Squares that touch in the net fold to faces that share an edge. The two ends of the column, the lid and the back, do not touch in the net, but they meet when it is folded: the back folds up and its top edge meets the edge of the lid.
Other solids, other nets
Other solids unfold into different nets. A square pyramid has a square base and 4 triangles, one standing on each edge of the base, which lean in to meet at the top point. Its net has 5 faces: 1 square with a triangle on each of its 4 sides.
The net of a square pyramid: 1 square base and 4 triangles.
The shapes name the solid
The shapes in a net tell you which solid it folds into. Six equal squares fold into a cube. Six rectangles in three matching pairs fold into a cuboid. Two triangles and three rectangles fold into a triangular prism: the triangles are its two ends, and the rectangles wrap round between them.
The net of a triangular prism: 2 triangle ends and 3 rectangles.
A curved surface lies flat too
A cylinder, the shape of a tin can, has two circles for its ends and one curved surface. Cut the curved surface straight down and unroll it, and it lies flat as a rectangle. The height of the rectangle is the height of the can, and its width is the distance all the way round a circle end, the circumference.
a closed cylinder: two lids of area πr² and a curved side that has no formula until it is laid flat
Unroll the cylinder and read the wrapper's width
Drag to unroll the cylinder. The curved surface flattens into a rectangle as wide as the circumference of the circle ends, and the two circles lie above and below it.
Worked example: Opposite Faces on a Cube Net
Question A cube net is a column of four squares numbered 1, 2, 3, 4 from top to bottom, with square 5 attached to the left of square 2 and square 6 to its right. When the net is folded into a cube, which face is opposite face 1? Which face is opposite face 5?
1.In the column, 1 and 3 have exactly one square between them: they fold to opposite faces. So do 2 and 4.
In the column, 1 and 3 have one square between them: opposite faces. So do 2 and 4. 2.In the row, 5, 2, 6: squares 5 and 6 have 2 between them, so they are opposite.
In the row, 5 and 6 have square 2 between them: opposite. 3.Opposite face 1: face 3. Opposite face 5: face 6.
Opposite 1 is 3; opposite 5 is 6. 4.Check: the three pairs 1-3, 2-4, 5-6 use all six faces once.
Three pairs, six faces.
Answer: 3; 6
Common mistakes
- Taking neighbors in the net, such as 1 and 2, as opposite: touching squares fold to touching faces.
- Pairing 4 with 1 because they are the two ends of the column: the ends fold round to become neighbors.