3D Shapes: Faces, Edges and Vertices Explained

Boxes, tins, balls and dice are all 3D shapes, so children handle them years before they learn the names. School maths adds three words for describing them: faces, edges and vertices. Once a child can count those on a real object, the names of the shapes are much easier to remember, because each shape has its own set of numbers.

What is the difference between 2D and 3D shapes?

A 2D shape is flat. It has a length and a width but no thickness, like a square drawn on paper. A 3D shape is solid: it also has depth, so you can pick it up and turn it round. The faces of most 3D shapes are 2D shapes. A cube is made of squares and a pyramid has triangles for sides. You can look at both kinds in the shapes explorer, with flat shapes on the 2D shapes page and solids on the 3D shapes page.

What are faces, edges and vertices?

• Face: a surface of the shape. A cube has 6 flat faces. Put a finger flat on each one to count them.
• Edge: a line where two faces meet. Run a finger along each one. A cube has 12.
• Vertex: a point where edges meet, the corner. A cube has 8. One is a vertex; two or more are vertices.

On the 3D shapes page you can tap faces, edges or corners and the shape lights up each one, which is a quick way to check a count.

How many faces, edges and vertices does each shape have?

Shape	Faces	Edges	Vertices
Cube	6	12	8
Cuboid	6	12	8
Triangular prism	5	9	6
Square-based pyramid	5	8	5
Tetrahedron (triangular pyramid)	4	6	4
Octahedron	8	12	6
Cylinder	3 (2 flat, 1 curved)	2	0
Cone	2 (1 flat, 1 curved)	1	1 (the apex, a point with no edges)
Sphere	1 curved	0	0

For the shapes with only flat faces, there is a neat check: faces plus vertices is always 2 more than edges. A cube gives 6 + 8 = 14, and 12 + 2 = 14. A square-based pyramid gives 5 + 5 = 10, and 8 + 2 = 10.

Do curved shapes have faces and edges?

This is the part where books disagree. Strictly, faces are flat and edges are straight, so a sphere has none. Many primary schools count a curved surface as a face, which gives the numbers in the table above: 3 for a cylinder, 2 for a cone and 1 for a sphere. If your child's homework says something different, go with the teacher's wording. What matters is that your child can say which surfaces are flat and which are curved.

What is the difference between a prism and a pyramid?

A prism has two matching ends and is the same shape all the way along. Slice it anywhere and the cut looks like the end. A cuboid is a prism with rectangle ends, and a triangular prism has triangle ends, like a tent. A pyramid has one base and its other faces are triangles that lean in to a single point, the apex. Pyramids are named after the base, so a square-based pyramid has a square underneath.

What is the net of a 3D shape?

A net is what you get when a shape is unfolded and laid flat. A cereal box cut along its edges and opened out is the net of a cuboid. Counting the pieces of a net is another way to count faces: the net of a cube has six squares. On the 3D shapes page, every shape except the sphere unfolds into its net and back, so children can see which face ends up where. Nets also link to area, because the area of the net is the surface area of the shape. There is more on that in area and perimeter explained.

How can you practise 3D shapes at home?

• Go on a shape hunt: a tin is a cylinder, a dice is a cube, a ball is a sphere, a cereal box is a cuboid.
• Count on real objects. Stick a small sticker on each face as it is counted, so none is counted twice.
• Open out a cardboard box to see its net, then fold it back up.
• Build shapes with straws and modelling clay: the straws are edges and the clay balls are vertices.
• Play "what am I?": "I have 5 faces, 9 edges and 6 vertices." (A triangular prism.)

Counting edges in equal groups is good times tables practice too. A cube has 4 edges on top, 4 on the bottom and 4 joining them, which is 3 × 4 = 12. For more shape questions, the shapes hub has a quick quiz, and printable worksheets cover the number work behind it.