Discussion
A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?
Answer: A
The answer is Only (i) can correspond to the unfolded cube in Panel I.
Fold the net with the diamond face at the front. The face above it in the net (small square in its top-right quarter) becomes the top, the topmost face (small corner triangle) becomes the back, the face below the diamond (thin wedge) becomes the bottom, the half-shaded face attached to the back becomes the right side, and the face with the diagonal half shaded becomes the left side.
Cube (i) is this cube turned a quarter turn about the front-to-back axis: the diamond stays in front, the diagonal-half face comes on top with its shaded half towards the front-right corner, and the small-square face moves to the right with the square in its lower back quarter, exactly as drawn.
Cube (ii) shows the corner-triangle face in front and the wedge face on top, which fixes the cube as the standard one turned half a turn about the left-right axis. The right face is then the half-shaded face, whose shaded half must lie along the bottom edge. Cube (ii) instead shows a vertical strip along the front edge, so it cannot come from this net. That rules out 'Only (ii)', 'Both' and 'Neither'.
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