Shape & Space
Exploring 3D Shapes: Faces, Edges, Vertices, and Nets
3rd Class · 4th Class · 5th Class · 6th Class
- ✓By the end of this lesson students will be able to identify and name common 3D shapes (solids).
- ✓By the end of this lesson students will be able to identify and count the faces, edges, and vertices of 3D shapes.
- ✓By the end of this lesson students will be able to describe the properties of common 3D shapes.
- ✓By the end of this lesson students will be able to recognise and draw simple nets for 3D shapes.
- ✓By the end of this lesson students will be able to match a 3D shape to its corresponding net.
Key concepts
3D shapes, also called solids, are shapes that have three dimensions: length, width, and height. They take up space and can be held. Examples include cubes, cuboids, cylinders, cones, and spheres.
A face is a flat surface of a 3D shape. Think of the sides of a box or the top and bottom of a tin can. Faces are 2D shapes like squares, rectangles, or triangles.
An edge is where two faces of a 3D shape meet. It's like the line or seam where two flat surfaces join together. Edges are straight lines.
A vertex (plural: vertices) is a corner of a 3D shape where three or more edges meet. It's a point. Think of the sharp points on a cube or pyramid.
A net is a 2D (flat) shape that can be folded along its edges to form a 3D shape. Imagine unfolding a cardboard box; the flat shape you get is its net. Each face of the 3D shape is part of the net.
Key facts to remember
- 13D shapes are also known as solids.
- 2A face is a flat surface of a 3D shape.
- 3An edge is where two faces meet.
- 4A vertex is a corner where three or more edges meet (plural: vertices).
- 5A net is a 2D shape that can be folded to make a 3D shape.
- 6A cube has 6 faces, 12 edges, and 8 vertices.
- 7A cylinder has 3 faces (2 flat, 1 curved), 2 edges (curved), and 0 vertices.
- 8A sphere has 1 curved face, 0 edges, and 0 vertices.
Worked examples
Example 1
Look at the cube below. How many faces, edges, and vertices does it have?
Answer
Faces: 6 Edges: 12 Vertices: 8
A cuboid has the same number of faces, edges, and vertices as a cube.
Example 2
Describe the properties of a triangular prism by stating the number of its faces, edges, and vertices.
Answer
Faces: 5 (2 triangles, 3 rectangles) Edges: 9 Vertices: 6
Visualising or holding a real triangular prism can help with counting.
Example 3
Which of the following nets would fold to make a square-based pyramid?
Answer
The net that has a central square with a triangle attached to each of its four sides will fold to make a square-based pyramid.
Drawing the net and cutting it out to fold can be a great way to check your answer.
Common mistakes
- ✗Confusing faces, edges, and vertices, especially when counting quickly.
- ✗Forgetting to count all the hidden faces, edges, or vertices on a diagram.
- ✗Assuming all 3D shapes have straight edges and flat faces (e.g., cylinders and spheres do not).
- ✗Incorrectly identifying a net, often by not visualising how the faces would connect when folded.
- ✗Counting a curved surface as multiple faces or a curved line as multiple edges.
Exam tips
- ★When counting faces, edges, or vertices, use your finger to point to each one as you count to avoid missing any or counting them twice.
- ★If possible, use real-life objects (like a box, a can, or a ball) to help you visualise and count the properties of 3D shapes.
- ★For nets, try to draw them on paper and imagine cutting them out and folding them. This helps you see if they will form the correct 3D shape.
- ★Always read the question carefully to ensure you are answering exactly what is asked, whether it's identifying, counting, or describing.
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