120. The Cube's Net · folding flat patterns into 3D solids
A net is a flat pattern that folds along its edges to form a 3D solid. These six congruent squares make one of the 11 distinct nets of a cube.
What this lesson covers
Try to break it
Drag the Fold slider all the way from NET to CUBE and back. However far you fold, the six squares always meet edge-to-edge with no gaps and no overlaps — that's what makes this flat pattern a valid net of a cube. Five edges in the net become five "spine" edges of the cube; the remaining seven cube edges form from pairs of free edges that meet up as you fold (5 + 7 = 12 cube edges).
How you build it
Build one of the 11 nets of a cube — a Latin-cross.
- Draw a square in the centre of the canvas — this is the base face.
- 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 BOTTOM square — the six squares form a Latin-cross net of a cube.
The proof, step by step
Prove that the net folds into a cube.
- A net must have exactly 6 faces for a cube.
- The faces must be connected edge-to-edge without gaps.
- When folded, each edge of the net meets exactly one other edge.
Worked example
A net is a 2D pattern that folds into a 3D solid. Which shape below can be folded to make a cube?
A cube has 6 faces. The only valid net among the options is the cross shape of 6 squares, which folds perfectly into a cube.
- A 2x3 rectangle of squares
- A cross shape of 6 squares — correct
- A straight line of 5 squares
- A 'T' shape of 5 squares