Which Nets Fold into a Cube?

0:00Which nets made of six squares fold up into a cube?

0:04A net is a flat shape that folds up into a solid. Here is a cube opened out flat.

0:12A cube has six faces, all squares, so its net has six squares: one, two, three, four, five, six.

0:22Now fold this cross shape along the edges between its squares.

0:27Each square becomes one face, with no gaps and no overlaps, so the cross is a cube net.

0:34Now try six squares in a row.

0:38Squares one to four wrap around into a tube.

0:42Then square five covers square one, and square six covers square two.

0:48Two faces overlap and both ends stay open, so a row of six is not a cube net.

0:55Next, try a block two squares high and three squares wide.

1:00Fold up the two end columns and you get a long open channel, not a cube.

1:06Open it flat again: here, four squares meet at one corner, but a cube has only three faces at each corner.

1:14So the block is not a cube net either. Six squares joined edge to edge do not always make a cube.

1:22In fact, there are exactly eleven different cube nets, if turned or flipped copies count as the same.

1:30A triangular prism folds up from two triangles and three rectangles.

1:38A cylinder rolls up from one rectangle and two circles.

1:46A cube net is six squares that fold into a cube with no gaps and no overlaps.