Cube Net Puzzles
Fold a flat net into a cube in your head. Which face ends up opposite which? Which of these shapes is even a net at all? Which cube could this net have made? Sixty patterns across five question types, with the folding worked out after every attempt.
Also known as net of a cube, cube views and cube folding — all the same puzzle.
Which Flat Nets Fold Into A Cube
A cube net is a flat arrangement of six squares that folds up into a cube. A cube net puzzle asks which nets fold correctly, which faces finish opposite each other, or what a folded cube looks like from a corner. There are exactly eleven distinct nets — every other six-square arrangement fails to close.
The Eleven Nets Of A Cube
There are 35 ways to join six squares edge to edge. Exactly eleven of them fold into a cube; the other 24 overlap themselves. Learning the eleven on sight is the single biggest win in this item type, and they come in four families:
- 1-4-1 — a row of four with one square on either side. Six of the eleven look like this, and it is the shape most people picture when they hear "net".
- 2-3-1 — a row of three with squares above and below. Three of the eleven.
- 2-2-2 — a staircase of three pairs. Just one, and the least net-like of the lot.
- 3-3 — two rows of three, offset by one. Also just one.
Anything with a 2×2 block of squares in it can never be a net, which is the fastest single test there is: four squares in a square would have to fold onto each other.
| Family | How many | Shape |
|---|---|---|
| Row of four, one square each side | 6 | The commonest, and the one everybody draws first |
| Row of three, with two and one | 3 | A staircase of three rows |
| Two rows of three, offset | 1 | The stepped double row |
| Staircase | 1 | Three rows of two, each shifted by one |
| Total | 11 | Out of 35 hexominoes — the other 24 will not fold |
How To Find The Opposite Face
- Roll a cube across the net. Put an imaginary cube on one square and tip it onto the next. The face touching the paper is the face that square becomes.
- Use the two-apart rule. In any straight run of squares, faces two apart are opposite. On a 1-4-1 net the row of four gives you two opposite pairs immediately.
- Remember every face touches four others. A face has exactly one face it never touches, and that is its opposite. So "which face never touches X" and "which is opposite X" are the same question.
- Turn a corner carefully. Squares that sit off the main run are where mistakes happen — roll to them rather than guessing from the flat picture.
The elimination that costs nothing. A cube shows at most three faces at once, and all three meet at a corner — so no visible pair can be opposite. Work out the three opposite pairs from the net first, and any cube showing two faces from the same pair is impossible. That usually removes half the options before you fold anything.
The Five Question Types
- Opposite faces — which face finishes on the far side from a given one. The commonest form by far.
- Touching faces — which face never meets a given one. The same question wearing a different hat.
- Which net folds — four six-square shapes, only one a genuine net.
- Which net fails — the reverse, and harder, because three valid nets look reassuringly similar.
- Net to cube — a folded cube drawn in three dimensions; only one of the four could have come from the net shown.
Why There Are Exactly Eleven Nets
A cube has exactly eleven distinct nets, and that number is not a convention — it falls out of the geometry. Take all 35 hexominoes (the ways six squares can join edge to edge), try to fold each one, and eleven succeed. They group as six, three, one and one by the arrangement of their rows. Knowing there are eleven is worth more than memorising them: if a shape in front of you is not one of the eleven, no amount of careful folding will help, and you can say so immediately.
Cube Net Puzzles Frequently Asked Questions
How many nets does a cube have?
Exactly eleven, out of the 35 possible six-square shapes. Six are 1-4-1, three are 2-3-1, one is the 2-2-2 staircase and one is the 3-3 offset double row.
Is there a quick way to rule a shape out?
Yes — if it contains a 2×2 block of squares it cannot be a net. Beyond that, roll a cube across it mentally; the moment two squares land on the same face, it fails.
Why can't a cube show two opposite faces at once?
Because the three faces you can see all meet at a single corner, and opposite faces point in exactly opposite directions. Any drawing showing both is impossible.
How many puzzles are there?
There is no fixed number. Each puzzle is rebuilt from the short seed in the page address, so the supply is effectively unlimited.
How do I work out which face is opposite which?
Roll a cube across the net in your head, one square at a time: the face touching the paper is the face that square becomes. On a straight run of squares, faces two apart are always opposite. Every face of a cube touches four others, so the only face it does not touch is its opposite.
Is it free and does it need an account?
It is completely free and there is no account. Nothing is uploaded; your score is kept only in your own browser.
What is a net of a cube?
A flat arrangement of six squares that folds up into a cube without any face overlapping another. Cut a cardboard box along enough edges to lay it flat and what you have is a net. Not every arrangement of six squares works, which is the whole puzzle — and there are exactly eleven that do, once rotations and reflections of the same shape are treated as one.