Match a marked cube

Use opposite faces and the order of marks around a corner to match a net to its cube.

Keep each mark on its face

A net has six squares. Fold along their shared edges to make a cube. Each mark stays on its own face. You may turn the whole cube in any direction.

Squares that share an edge in the net stay adjacent after folding. Opposite faces never share an edge. Each cube view shows three faces meeting at one corner; the front face appears on the left of the drawing.

In this net, the opposite pairs are square and ring, plus and dot, and four dots and cross.

The flat net.
One possible folded view.

Check faces, then corner order

Cube A is possible: cross is on top, ring is on the front, and plus is on the right.

Cube B puts plus and dot on faces that meet. Those marks are opposite in this net, so they cannot meet at an edge.

Cube C keeps cross on top but swaps the front and right marks of A. This reverses their order around the shared corner. Turning the cube cannot do that; it would require a mirror image.

The flat net.
A: possible.
B: opposite faces meet.
C: corner order reversed.

Match a new net

Fold this new net and compare A with B. Check opposite faces first, then the order of the three marks around the visible corner.

A new net.
Cube A
Cube B

Try it

Which cube can this new net make?

  1. Cube A
  2. Cube B
Show the answer

Cube A

Yes. Cube A keeps the same three marks in a possible order around the corner. The other view swaps two of them, creating a mirror image.

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