Concept 6 of 6
Cube Nets: Unfolding the Box
Today's big idea
Only 11 arrangements of 6 squares actually fold up into a cube.
Plus shape folds cleanly; the 3 by 2 block overlaps and does not.
How it works
👀 What's going on?
Take an empty cereal box and cut along its edges until it lies flat on the table. That flat shape is called a net: the box, unfolded. A cube has 6 square faces, so a cube's net is always 6 squares joined edge to edge. Here is the catch. You can join 6 squares in loads of ways, and most of them will not fold back into a cube.
💡 Here's the trick
Look at the two shapes above. Both are made of exactly 6 squares. The plus shape folds up perfectly, and each of its 6 squares becomes one face of the cube. The 3 by 2 block cannot fold up. As you close it, two squares land on the same face and others are left with nothing to cover. Out of every shape you could make from 6 squares, only 11 actually fold into a cube.
🪄 How to do it
- 1.Count the squares in the picture above; a cube net always has exactly 6.
- 2.Pick one square as the base, then fold the other five up around it in your head.
- 3.Check that every square lands on a different face, with none left over and no two clashing.
✍️ Try it
Does a straight line of 6 squares in a row fold into a cube? And does a row of 4 squares with one extra square on top of the first and one under the last?
The straight line does not fold. Curl it round and the 5th square lands back on the 1st, so two squares fight for one face. The row of 4 with a flap at each end does fold, and it is one of the 11.
⚠️ Watch out
It is tempting to think the two ends of a row end up opposite each other. In a row of 4 they do not. Wrap it round the cube and the ends meet as neighbours. In a straight strip it is the squares two apart that land on opposite faces.
🌟 Why this matters
Every cardboard box, juice carton and gift box begins life as a flat net that a machine folds up. Get the net wrong and none of them close. Folding a shape in your head is the same skill designers use to plan packaging.
Exam tip: Count the squares first. Anything that is not exactly 6 squares is ruled out before you fold a thing.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A row of 4 squares has one square on top of the first and one under the last. Does it fold into a cube?”
- 1
Picture the net
Four squares in a row make a band, plus one flap on each end square.
- 2
Fold the row into a ring
The four squares wrap round into the 4 side walls of the cube.
- 3
Fold the two flaps
The flap on top of the first square closes the top, and the flap under the last closes the bottom. No overlaps. ✓
- 4
Answer ✓
Yes — all 6 faces land in place, so it folds into a cube.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Imagine folding each net into a box. 11 nets work for a cube — others overlap or leave gaps.
Sorted: 0 of 4
Quick check
✅ VERIFICATION
Four squares sit in a straight row inside a cube net. Which one ends up opposite the 1st?
⚡ Finish the activity above first to answer.
Keep going!