NVR: cube nets and cube views

Watch it happen

Fold a net in your mind

Six squares joined edge to edge — a cube net. Fold it up in your mind: some faces land on opposite sides of the cube and never touch each other.

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The idea

When a flat net folds into a cube, every square becomes one face. Your first job is not to fold everything at once. Find the faces that end up opposite each other, because opposite faces can never touch and can never be seen together in one cube view.

Use this routine. First, look for a straight strip of four squares: it wraps around the cube, so the first and third squares in the strip are opposite, and so are the second and fourth. Next, look for two squares sticking out on opposite sides of the same square: those two flaps are also opposite each other. The two squares left over are the last opposite pair.

Now test answer choices against those pairs. If a cube view shows two opposite faces side by side, it is impossible, however neat it looks. If a net has seven squares, or a straight strip of five or six, it cannot fold without overlap, so reject it at once.

Worked example

The net in the picture folds into a cube. Which face ends up opposite the a half-black face (face A)?

1. Here is the net of a cube, flattened out. The master rule: two faces that end up opposite each other on the cube never touch and never share an edge in the net.

   

2. First pair, highlighted: the a blank face (face C) and the a dot in the centre (face E). Fold the strip round in your mind and they land face to face on opposite sides.

   

3. Second pair, highlighted: the a cross (face B) and the an arrow pointing to one edge (face D). That leaves exactly two faces unclaimed.

   

4. Two faces left, so they must be opposite each other — a cube has exactly three pairs of opposite faces and no face is left over. The last picture colours all three pairs.

   

Answer: The a triangle pointing to one edge (face F) — the three pairs are a blank face & a dot in the centre, a cross & an arrow pointing to one edge, and a half-black face & a triangle pointing to one edge.

Try one yourself

Same net as the worked example. Which face is opposite the a blank face (face C)?

Watch out

• Faces that share an edge in the net fold to sit side by side, not opposite each other.
• A cube view showing two opposite faces together is impossible, even if the drawing looks tidy.
• Do not guess opposite faces by distance alone — always use the strip-of-four and opposite-flaps rules.