Recognition of Solids
72. From Flat to 3D · Discover how nets build solids
The net folds into a cube.
A net of a 3D solid is its 2D unfolded outline — what the solid looks like when laid flat. The net for a cube is 6 connected squares; fold along the edges and you get back the cube.
What this lesson covers
Try to break it
Slide the fold control back and forth. However far you fold it, the six squares always wrap into one closed cube with no gaps or overlaps — that is what makes this flat pattern a true net of a cube.
How you build it
Construct a cube net from six squares.
- Draw a square in the centre — this is the base.
- Attach a square to the top edge of the base.
- Attach a square to the bottom edge of the base.
- Attach a square to the left edge of the base.
- Attach a square to the right edge of the base.
- Attach the sixth square to the outer edge of the top square — the six squares form a cube net.
The proof, step by step
Prove that the net folds into a cube.
- A net is a 2D pattern made of faces.
- Folding along shared edges brings faces together.
- A cube net has exactly 6 squares.
- Not all arrangements of 6 squares form a valid cube net.
Worked example
Which of the following patterns can be folded to form a closed cube?
A valid cube net must have exactly 6 squares arranged so they fold without overlapping. The cross shape is the classic pattern that folds perfectly into a cube, while a single row of 6 squares would cause faces to overlap and cannot form a closed cube.
- A row of 4 squares with 1 square attached to the top of the second square.
- A 'T' shape made of 5 squares.
- A single row of 6 squares.
- A cross shape made of 6 squares. — correct