Last reviewed 22 Sept 2026 · 6 min read
What the topic asks
Three families of question:
- Turning a figure — how does it look after a rotation, or from the opposite side?
- Views of a solid — what does it look like from the top, the front, or a side?
- Position and facing — after a series of turns, which way is a person or object facing, and what is in front of them?
Rotation without drawing
Fix on one asymmetric feature — a notch, an arrow, a shaded corner — and ask where that single feature goes. A clockwise turn sends the top to the right, the right to the bottom, the bottom to the left, and the left to the top. Applying that once to one feature is enough to reject most options.
Three marks reading A, B, C clockwise still read A, B, C clockwise after any rotation. If an option shows them anticlockwise, it is a mirror image and cannot be the answer to a rotation question.
Views of a solid
For a stack of cubes:
- The top view shows how many columns there are and where, not how tall they are.
- The front view shows the height of the tallest column in each left-to-right position.
- The side view shows the height of the tallest column in each front-to-back position.
A view is a silhouette: two different stacks can share a view, which is why a question gives two or three views together.
Counting hidden blocks
In a stack drawn in perspective, count layer by layer from the bottom, not cube by cube from the picture. A cube that supports another must exist even if it cannot be seen — that is the whole point of the question. State the number of cubes in each layer, then add.
Nets
A net folds into a solid when the faces meet without overlapping. For a cube, the practical tests are:
- Exactly six squares.
- No four squares meeting at a point in a block.
- In a row of four squares, the first and third, and the second and fourth, end up opposite.
Position and facing
These are direction questions in disguise. Keep a small arrow for the facing direction and update it at each turn; then read what lies ahead, to the left and to the right from the figure's point of view, not the reader's.
Worked examples
A square has a notch on its top edge. Where is the notch after a clockwise turn?
Solution. On the right edge.
An arrow points north-west. Where does it point after a turn?
Solution. South-east.
A stack has 3 cubes in one column, 2 in the column to its right and 1 in the column behind the first. What does the top view show?
Solution. Three filled positions — one behind and two side by side — with no heights; the top view shows only which positions are occupied.
For the same stack, what is the front view?
Solution. Two columns, of heights 3 and 2 — the cube behind is hidden behind the taller column of 3.
A stack is built as 6 cubes in the bottom layer, 3 in the middle and 1 on top. How many cubes in all, and how many are hidden from a single viewpoint?
Solution. 10 cubes. From any one viewpoint at least the cube at the back of the bottom layer is hidden, so the count must come from the layers, not the picture.
A net has six squares in a row. Can it fold into a cube?
Solution. No — a straight row of six leaves two faces to overlap; a cube net needs at most four in a row with the other two attached on the sides.
In a net of four squares in a row (P, Q, R, S) with T above Q and U below Q, which face is opposite Q?
Solution. S — the first and third are opposite (P and R), and the second and fourth (Q and S). T and U are opposite each other.
A person faces east, turns anticlockwise, then . Which way do they face?
Solution. East → north → south.
Two people face each other. One raises the hand on her own left. From the other person's point of view, which side is it on?
Solution. Their right — facing figures have their left and right reversed relative to each other.
A figure's three marks read X, Y, Z clockwise; an option shows Z, Y, X clockwise. Can it be a rotation of the original?
Solution. No — the order is reversed, so it is a mirror image.