The Cuboid

A stretched cube

Every face of a cube is a square. Now stretch the cube in one direction, so it grows longer. The four faces along the stretch grow into long rectangles. The solid is now a cuboid.

A brick is a cuboid. So are a tissue box, a cereal box and a book. Each one is a solid with flat faces, and the faces are not all squares.

The cube has 6 square faces. The cuboid is stretched, so its faces are not all squares, but it still has 6 of them.

Pulled out along one edge, the cube keeps its 6 faces. The 2 end faces stay squares, and the 4 faces along the stretch become rectangles.

Six faces, in pairs

A cuboid has 6 flat faces, the same number as a cube. They come in matching pairs: the top and the bottom, the front and the back, and the two ends. Each face has a partner the same size and shape on the opposite side.

From one place you can see only 3 of the faces: the top, the front and one end. The other 3 are hidden on the far side. Counting only the faces you can see gives 3, which is half the answer. Count in pairs instead: 2 + 2 + 2 = 6.

The 6 faces of a cuboid are numbered. The gold numbers are on the 3 faces you can see, and the gray numbers are on the 3 hidden on the far side.

Cube or cuboid?

To name a box, look at its faces. If every face is a square, it is a cube. If the faces are flat but some of them are longer than they are wide, it is a cuboid.

Every face of a cuboid is flat, so a cuboid does not roll. It is flat on top and flat underneath, so cuboids stack well. That is why bricks are cuboids: they sit one on another to build a wall.