Start here · the first lesson of Dice: views, opposite faces and open nets
Dice: views, opposite faces and open nets
Cubes and Dice · for IPMAT Indore, IPMAT Rohtak and JIPMAT
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The idea
A die (cube) has three pairs of opposite faces. Questions show two to four views of the same die, or an unfolded sheet (net), and ask which face is opposite another, which face is on top when another is at the bottom, or which drawn die can be made from the net. Rohtak 2019–2020 and JIPMAT 2024–2026 each asked one or two (JIPMAT 2025 Q7: four views, opposite of 3).
Textbook vs exam method
Textbook method
- Neighbours. Faces seen together in a view are adjacent. Collect the neighbours of each face; a face with four known neighbours is opposite the sixth.
- Common faces. Two views sharing two faces: the third faces are opposite. Sharing one face: write each view clockwise from that face; the second faces are opposite, and so are the third faces.
- Nets. Fold mentally: in a row of three or four squares, alternate squares are opposite; squares attached to the row become the remaining faces. For a full picture, fold around one square and track where each neighbour goes.
- Standard dice. Opposite faces add to 7, so a view never shows 1 with 6, 2 with 5 or 3 with 4; the hidden bottom = 7 − top.
Exam method
- Strike out every face seen next to the asked face; often one option survives.JIPMAT 2024
- If two remain, use the clockwise reading from a common face (PW and afterboards solutions use the same rule).
- For nets, mark the opposite pairs on the sheet first (pairs two apart in a row), then reject every option that shows an opposite pair together.
- Corner order decides the last option: on the sheet, read the three faces round a shared corner clockwise; on a drawn die read top → right → front. A die showing the reverse order is the mirror image.