What is a prism?
A prism is a 3D shape with two identical ends and flat sides, which is the same shape all the way through.
The answer
For a prism whose ends have n sides: n + 2 faces, 3 × n edges and 2 × n vertices. A triangular prism has 5 faces, 9 edges and 6 vertices.
Prism diagram and properties
| Property | Count |
|---|---|
| Faces2 triangles and 3 rectangles on the triangular prism drawn | 5 |
| Flat faces | 5 |
| Curved faces | 0 |
| Edges | 9 |
| Vertices (corners) | 6 |
Key facts about the prism
- A prism is named after its end: a triangular prism has triangle ends, a pentagonal prism has pentagon ends.
- If you slice a prism anywhere parallel to its ends, the slice is the same shape as the ends.
- A cuboid is a rectangular prism, and a cube is a square prism.
- A cylinder is not a prism, because it has a curved face.
Faces, edges and vertices of prisms
For a prism whose ends have n sides: faces = n + 2, edges = 3 × n, vertices = 2 × n. Every row passes Euler's check: vertices − edges + faces = 2.
| Shape | Faces | Edges | Vertices |
|---|---|---|---|
| Triangular prism | 5 | 9 | 6 |
| Square prism (cuboid) | 6 | 12 | 8 |
| Pentagonal prism | 7 | 15 | 10 |
| Hexagonal prism | 8 | 18 | 12 |
Where you see it
A Toblerone box is a triangular prism, and so is a tent. A pencil before it is sharpened is often a hexagonal prism.
The common mistake
Naming the prism after its side faces. The sides are always rectangles; it is the shape of the two ends that gives the prism its name.
An 11+ style question
A prism has 7 faces. What shape are its two ends?
Answer: Pentagons
- A prism has 2 end faces plus one rectangle for every side of the end shape.
- 7 − 2 = 5 rectangles, so each end has 5 sides.
- It is a pentagonal prism: its ends are pentagons.
Related shapes and skills
More shapes
Questions parents ask
How many faces, edges and vertices does a prism have?
It depends on the shape of its ends. For a prism whose ends have n sides: n + 2 faces, 3 × n edges and 2 × n vertices. A triangular prism has 5 faces, 9 edges and 6 vertices. The same counting works for any prism: a hexagonal prism has 6 + 2 = 8 faces, 3 × 6 = 18 edges and 2 × 6 = 12 vertices.
Is a cylinder a prism?
Not at primary school. A prism has flat faces only, and a cylinder has a curved face. It does share one prism fact: every slice across it is the same circle.
Shape questions are quick marks in the 11+
Angles, symmetry, nets and 3D shapes come up in 11+ maths and non-verbal reasoning. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.