What is a tetrahedron?
A tetrahedron is a 3D shape with four triangle faces. It is the same shape as a triangular-based pyramid.
The answer
A tetrahedron has 4 faces, 6 edges and 4 vertices.
Tetrahedron diagram and properties
| Property | Count |
|---|---|
| Faces4 triangles | 4 |
| Flat faces | 4 |
| Curved faces | 0 |
| Edges | 6 |
| Vertices (corners) | 4 |
Key facts about the tetrahedron
- Tetrahedron and triangular-based pyramid are two names for the same shape.
- Any face can be the base, because every face is a triangle.
- In a regular tetrahedron all four faces are identical equilateral triangles.
- Three faces meet at every vertex, and it has fewer faces than any other solid with flat faces.
Where you see it
Four-sided dice used in board games and pyramid-shaped tea bags are tetrahedrons.
The common mistake
Counting 3 faces because the drawing shows only the sloping ones. The base is a face too, so a tetrahedron has 4.
An 11+ style question
A tetrahedron is made from straws for the edges and balls of modelling clay for the vertices. How many straws and how many balls are needed?
Answer: 6 straws and 4 balls
- The base triangle has 3 edges, and 3 more go up to the top point: 3 + 3 = 6 straws.
- There are 3 corners on the base and 1 at the top: 3 + 1 = 4 balls.
- Check with Euler's rule, which works for solids like these, with flat faces and no holes: vertices take away edges, add faces, always makes 2. Here 4 − 6 + 4 = 2.
Related shapes and skills
More shapes
Questions parents ask
How many faces, edges and vertices does a tetrahedron have?
A tetrahedron has 4 faces, 6 edges and 4 vertices. Its net is 4 triangles. For a regular tetrahedron, one way to draw it is a big equilateral triangle split into 4 smaller ones by joining the middles of its sides.
Is a tetrahedron a pyramid?
Yes. It is a pyramid on a triangle base, so it is also called a triangular-based pyramid.
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.