Cube Unfolding

Identifying which 2D net corresponds to a given 3D cube.

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Identifying which 2D net corresponds to a given 3D cube.

Cube unfolding is the reverse of cube folding. Given a 3D cube with marked faces, you must identify which 2D net (unfolded pattern) would produce that cube when folded. This requires understanding the spatial relationships between cube faces and how they map to positions in the net.

net = unfold(cube, visible_markers)

A cube showing star, dot, and stripe patterns matches net with those markers in adjacent positions
Opposite faces in a cube are never adjacent in any valid net
The same cube can unfold into 11 different valid net patterns

How to recognize it

Identify the three visible faces and their markers
Find nets where those markers appear in correct relative positions
Eliminate nets with markers in impossible positions
Remember that opposite cube faces are separated by one face in nets

Common mistakes

Not accounting for marker orientation after folding
Forgetting that opposite faces can't be adjacent in nets
Confusing which face becomes top, front, or side

Step-by-step walkthrough

A cube shows a star on front, a circle on top, and a triangle on the right side. Which net could fold into this cube?

Note the three visible faces and their positions: star (front), circle (top), triangle (right).
These three faces share a common corner on the cube, so they must be adjacent in the net.
In any valid net, the star, circle, and triangle must all touch each other.
Eliminate nets where these three faces are not all mutually adjacent.
Check marker orientations: when folded, markers must align correctly with the original cube.

Answer: The net where star, circle, and triangle are mutually adjacent with correct orientations

Practice guidance

Spatial Reasoning