Sheet 14 of 14 · Non-verbal Reasoning
Cubes, nets and 3D shapes
Folding nets, counting cubes, views from above and paper folding. 10 rules, each with a worked example.
Cube nets
Opposite faces
Opposite faces never touch in the net
- In a straight line of three squares, the 1st and 3rd are opposite
Faces that meet
Two squares that touch only at a corner in the net share an edge on the cube
Nets that won't fold
A cube net has exactly 6 squares, never a 2 × 2 block, and never more than 4 in a row
Tip: There are 11 different cube nets.
Matching cube views
Faces seen together in one picture can't be opposite each other
ExampleIf one picture shows face A next to face B, then A and B are not opposite
3D shapes
Counting cubes
Count layer by layer, including hidden cubes holding the others up
ExampleA 3 × 2 bottom layer with 2 cubes on top = 6 + 2 = 8 cubesView from above (plan)
From above you see the top of every column: one square per column
ExampleThree columns in an L shape look like an L of 3 squares from aboveFront and side views
From the front you see how tall each column is, but not how deep
ExampleTwo cubes, one behind the other, look like 1 square from the frontFaces, edges and vertices
Cube 6, 12, 8 · square-based pyramid 5, 8, 5 · triangular prism 5, 9, 6
Tip: Faces + vertices − edges = 2, so you can check your counting.
Folding paper
Punched holes
Unfold one step at a time: each fold doubles the holes, mirrored in the fold line
ExampleFolded in half once and punched once → 2 holes, mirror images across the foldFolded shapes
The folded part flips over the fold line, like a reflection
Want the full explanation?
The study guide goes through each rule step by step, with more examples.