Properties of 3D Shapes & Nets
Recognising 3D shapes, counting faces, edges and vertices, and identifying nets.
What is Properties of 3D Shapes & Nets?
3D shapes have three dimensions: length, width and height. In the 11+ exam, you need to recognise common 3D shapes, count their faces, edges and vertices, and identify which 2D nets fold into which 3D shapes.
Common 3D shapes include cubes, cuboids, cylinders, cones, spheres, triangular prisms and square-based pyramids.
Step-by-Step Method
Learn the key 3D shapes
Cube (6 square faces), cuboid (6 rectangular faces), triangular prism (2 triangular + 3 rectangular faces), square-based pyramid (1 square + 4 triangular faces), cylinder, cone, sphere.
Count faces, edges and vertices
Face = flat surface. Edge = where two faces meet. Vertex = a corner point (plural: vertices).
Use Euler’s formula to check
F + V = E + 2 (Faces + Vertices = Edges + 2). This works for all polyhedra.
For nets, check which faces are adjacent
When a net folds up, faces that share an edge on the net will be adjacent on the 3D shape.
Opposite faces never share an edge on a net
This is the key rule for cube nets: if two squares share an edge, they cannot be opposite faces.
Worked Examples
How many faces, edges and vertices does a triangular prism have?
Working
- Faces: 2 triangles + 3 rectangles = 5 faces.
- Vertices: 3 on each triangle = 6 vertices.
- Edges: 3 on each triangle + 3 connecting them = 9 edges.
- Check: F + V = 5 + 6 = 11. E + 2 = 9 + 2 = 11. Correct!
Does a cylinder have any vertices?
Working
- A vertex is a point where edges meet.
- A cylinder has 2 flat circular faces and 1 curved surface.
- The circular edges are curved, not straight, and do not meet at points.
There are 11 different nets that fold into a cube. Which is the most common mistake?
Working
- A common wrong net is a 2×3 block of squares (a cross shape missing corners).
- To check: any row of 4 squares in a line is fine. The remaining 2 must not be directly opposite each other when folded.
Common Mistakes
Confusing faces and surfaces – a cylinder has 2 flat faces but also 1 curved surface.
Be precise: a cylinder has 2 flat circular faces and 1 curved surface, giving 3 surfaces total.
Miscounting edges on complex shapes.
Use Euler’s formula (F + V = E + 2) to check your count.
Assuming any arrangement of 6 squares forms a cube net.
Only 11 of the 35 possible hexomino arrangements actually fold into a cube.
Top Tips
- Memorise the faces/edges/vertices for common shapes: cube (6/12/8), cuboid (6/12/8), triangular prism (5/9/6), square pyramid (5/8/5).
- Euler’s formula F + V = E + 2 is a quick way to check your counting.
- For cube nets, remember the “no four in a square” rule – if any four squares form a 2×2 block, it is NOT a valid cube net.
- A prism has the same cross-section all the way through. A pyramid comes to a point at the top.
Ready to practise?
Put these techniques into action with our free practice papers.
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