Definition
Net of a solid
A net of a solid is a flat arrangement of its faces that can fold to make the solid.
What it means
Imagine carefully opening a cardboard box along some edges and pressing it flat. The connected flat faces you see are a net. Fold the same joins back up and the faces meet to rebuild the solid. A valid net stays connected, uses every face once, and closes without faces landing on top of one another.
Remember it
Open a box flat; fold the same edges back.
Example
Put one square in the middle, attach one square to each of its four sides, and attach a sixth square to the outer edge of the top square. Fold the four side squares up around the middle square, then fold the sixth square over the opening. The six faces meet to make one cube, so the pattern is a cube net.
Watch for
A pattern is not a valid net if folding makes two faces overlap or leaves the faces unable to close the intended solid.
Common mix-up
A net is not just a flat picture of a 3-D shape. It shows the actual faces joined in a pattern that can be folded.
Exact meaning
A net of a solid is a connected two-dimensional arrangement of all the solid’s flat faces, each used once and joined along edges, that folds into the intended three-dimensional solid without any two faces overlapping.