Numerical reasoning
Cube net questions: opposite faces, rotations and worked examples
A cube net question may ask for an opposite face or a possible view of the folded cube. Those are different tasks: opposite pairs help you eliminate options, but matching a marked cube also needs a consistent orientation. Work through one original net below.
Which face is opposite? Start with one net
Treat the numbers as face labels. Fold with the marks on the outside. Hold 3 at the front and 1 at the top: 2 becomes the left face, 5 the right, 4 the back and 6 the bottom.
A method for checking the options
Keep the same net for the next two questions. Read each triple in the order front, top, right; exchanging two positions changes the proposed view.
- Write the three opposite pairs. An option showing both faces of any pair together at a visible corner is impossible.
- For options that survive, align two adjacent reference faces, such as the front and top. Then check the third face.
- If the faces have arrows or other directional marks, check their direction after folding too. Our examples identify faces by number only.
Can the net make this cube? Opposites are not enough
Each row below describes the three visible faces of an option. Use the net above, with its marks facing outwards.
| Option | Front | Top | Right |
|---|---|---|---|
| A | 3 | 1 | 5 |
| B | 3 | 1 | 2 |
| C | 3 | 4 | 5 |
| D | 3 | 1 | 6 |
What changes when you turn the cube?
Now keep 1 on top and turn the same cube until 5 is at the front. Do not swap face labels or turn an individual face by itself.
Why one reference face is not enough
If you know only that 3 is at the front, the right face is not fixed. Rotating around that front face can place 1, 2, 5 or 6 on the right; 4, its opposite, stays at the back. An instruction such as “1 on top” removes that freedom.
Do opposite dice faces always add up to seven?
Cognik’s cube-folding practice constructs dice whose opposite pairs add up to seven. That is a rule of this exercise family, not a rule you can impose on every marked cube in another test. Follow the supplied net and instructions; arbitrary numbers or letters need not form conventional dice.
Common mistakes to check
Do not treat the ends of a four-face strip as opposites: here 2 and 4 touch after folding. Do not accept a view just because it contains no opposite pair. Turning the sheet or the whole cube preserves its relationships; swapping labels or reflecting the corner does not.
Practise the fold, then check your reasoning
Use this as untimed learning before adding a time limit. A physical paper model can check an answer, but predict the answer before folding so the check reveals what you misunderstood.
- Copy the six marked squares, keep their arrangement and fold with the numbers outside. Check the three opposite pairs and the reference corner 3–1–5.
- Turn your model while keeping 1 on top. Verify the view 5–1–4, then compare it with the mirrored option B.
- In Cognik, practise cube folding with new nets and review the explanation for each option. Use your own test’s instructions for its timing, scoring and permitted materials.
Further practice and sources
The worked examples in this guide are original and use the rules of Cognik’s cube-folding exercises. The University of Cambridge’s NRICH activity below offers further practice in predicting how nets fold; its questions and diagrams are not reproduced here.
Put it into practice
Explore more questions and step-by-step explanations in Cognik.
