Nets of Solids

Unfolding a solid

A net is the flat 2D shape you get when you unfold a solid and lay all its faces out side by side. Fold the net back up along its edges and you get the solid again. Each face of the solid appears exactly once in the net.

For example:

a cube unfolds into 6 squares (often arranged in a cross or a T shape);
a cuboid unfolds into 6 rectangles;
a triangular prism unfolds into 2 triangles and 3 rectangles.

One piece per face

Because every face shows up once, the number of pieces in the net equals the number of faces of the solid. Counting the pieces of a net is the same as counting the faces.

A net folds up into the solid, with one flat piece per face:

the number of pieces in the net = the number of faces of the solid;
a cube has a net of 6 squares — and there are 11 different valid cube nets;
a triangular prism has a net of 2 triangles + 3 rectangles.

See the net

Step through the figure. First a cube flattens into its six squares; then a triangular prism unfolds into two triangles and three rectangles. Count the pieces — that is the number of faces.