Fix One Face, Fold Its Neighbors

You almost never fold a whole pattern. You pin one square to one face of the solid, fold its neighbors around it, and stop as soon as the four drawings have run out of things to disagree about.

Pick the anchor

The anchor is the square you hold still. A good anchor is easy to find again in every drawing and touches as many other squares as it can. That gives you two candidates and no third: the most distinctive marked square — the black one, the one with the diagonal — or, on a pattern with no shading at all, the central square of the layout. The middle of a run of four squares touches four other squares; a square on the end of the run may touch only one.

Then commit. Assign the anchor to one named face of the solid — say it in words, "the black square is the top" — and keep it on that face for the whole item, through all four drawings. Nothing in the item forces the choice, so it is yours to make once. Re-seat the anchor halfway through and every conclusion you reached before the switch is worthless.

Fold the neighbors, one shared edge at a time

A square that shares an edge with the anchor swings up on that shared edge and lands on a face touching the anchor's face. Every flap turns away from you, so the solid closes up behind the sheet with the printed side outward — the rule from the previous lesson. Once the anchor is placed, that rule leaves each neighbor exactly one place to go.

Step through it below. The pattern is a run of four squares with one square above the run and one below. The gray square is the anchor, and it is the top face of the cube in every single drawing; each step blackens one more square and turns the cube on the spot — the anchor never leaves the top — until the blackened face comes around to meet you.

Walking a net, one shared edge at a time Step 1 of 6

1. Pin the anchor

The center square of the layout touches four of the other five. Call it the top face. Nothing has been folded yet and one face is already settled.

Pattern: the anchor

Anchor on top

The anchor is the center square of the layout; call it the top face and leave it there.

2. Fold the square to its right

It swings up on the edge the two squares share and lands on the face to the right of the anchor. Shared edge on the flat pattern, shared edge on the cube — that is the entire move.

Pattern: right neighbor black

Anchor on top, neighbor right

The square to the right of the anchor folds up to the right-hand face.

3. Fold the square above it

Turn the cube a quarter turn on the spot to bring that face around. The anchor is still on top, exactly where you left it; the square that sat above the anchor on the pattern is now the face on the right.

Pattern: top neighbor black

Anchor on top, neighbor right

The square above the anchor lands on a different side; the cube is turned so it faces you.

4. Fold the square to its left

Another quarter turn, another neighbor. Notice what has not happened: you have not re-folded anything, and you have not moved the anchor.

Pattern: left neighbor black

Anchor on top, neighbor right

The square to the left of the anchor, brought into view by another quarter turn.

5. Fold the square below it

The fourth and last neighbor. Four squares touched the anchor on the flat pattern; four faces touch the anchor's face on the cube, one on each of its edges.

Pattern: bottom neighbor black

Anchor on top, neighbor right

The fourth and last neighbor: the square below the anchor.

6. The square that is not a neighbor

The far end of the run shares no edge with the anchor, so it is not one of the four. It is the face opposite the anchor, and turning it into view sends the anchor out of sight — the opposite-face rule from the previous lesson, seen from the front.

Pattern: the far square

Anchor now hidden

The one square that touches no edge of the anchor: to see it, the anchor has to go out of sight.

All six steps are printed one below another if this stepper does not respond.

Two things fall out of that walk. The anchor's neighbors are exactly the squares that share an edge with it on the pattern — you can count them flat, before folding anything, and the count never changes. And you rarely need all four: a drawing of a cube shows three faces at once, so two of them named is usually the end of the item.

Work from the options inward

The four drawings are not there to be reproduced. They are there to be interrogated. Take one and read it as a claim about the anchor and its neighbors:

The pattern

What a drawing claims

Three shades, three faces in view: everything this drawing claims is a claim about the anchor's neighbors.

This drawing claims two things: the gray face touches the black one on its right, and the stippled face touches the black one on its left. Now go back to the pattern and test the claims. The gray square is edge-to-edge with the black square, and so is the stippled square, so this drawing has said nothing the pattern contradicts. A drawing that pressed a shade against the anchor where the pattern keeps those two squares apart would be finished on the spot — and you would never have folded the other three faces to prove it.

That is the direction of travel: read a drawing, get one claim out of it, test the claim on the pattern. Folding the whole pattern first and then hunting for the drawing that matches is the slow way round, and it makes you fold faces that no drawing ever asks about. Try it on real patterns in the pattern folding practice generator.

The takeaway

Choose one square — the most distinctive mark, or the center of the layout — assign it to one named face of the solid, and hold it there for the whole item. Its neighbors are exactly the squares that share an edge with it, and each one lands on the face touching the anchor across that shared edge. Read the drawings first so they tell you which neighbors are worth checking. Two or three faces settle most items; folding all six is a cost you never have to pay.

Fix One Face, Fold Its Neighbours

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