Describe features (faces, edges, vertices)
Theory
Describing 3D objects is a Year 3 maths space skill: every solid can be described by its faces (flat surfaces), its edges (where two faces meet) and its vertices (corners). This page explains how to count these features for cubes, prisms, pyramids, cylinders and cones. Curriculum: VC2M3SP01 / AC9M3SP01.
A 3D object is a solid shape that takes up space, like a box, a ball or a can. We describe a solid by looking at three features: its faces, its edges and its vertices.
A face is a flat surface of the solid. A cube has 6 flat, square faces. An edge is a line where two faces meet (on a cube it is straight), and a cube has 12 edges. A vertex is a corner, where edges meet, and a cube has 8 vertices. One corner is a vertex; two or more are called vertices.
Some solids have a curved surface as well. The rounded side of a cylinder or a cone is a curved surface, not a flat face. Only flat surfaces are counted as faces. Where a flat face meets a curved surface there is a curved edge.
You do not need a formula to describe a solid, but it helps to know the feature counts for the common shapes. To describe a solid, count its faces, then its edges, then its vertices.
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Rectangular prism | 6 | 12 | 8 |
| Triangular prism | 5 | 9 | 6 |
| Square pyramid | 5 | 8 | 5 |
| Triangular pyramid | 4 | 6 | 4 |
| Hexagonal prism | 8 | 18 | 12 |
| Cylinder | 2 flat, 1 curved | 2 (curved) | 0 |
| Cone | 1 flat, 1 curved | 1 (curved) | 1 |
How to describe a 3D object
- Count the faces. Find every flat surface, including the ones you cannot see at the back. A round side is a curved surface, not a flat face.
- Count the edges. An edge is a line where two surfaces meet. Count each one, including the hidden edges.
- Count the vertices. A vertex is a corner, where edges meet. Count each corner to get the number of vertices.
| \(6 - 3\) | \(=\) | \(3\text{ hidden faces}\) |
| \(8 - 7\) | \(=\) | \(1\text{ hidden vertex}\) |
A cube always has \(6\) faces and \(8\) vertices, so \(3\) faces and \(1\) vertex are hidden.
| \(\text{front triangle}\) | \(=\) | \(3\text{ edges}\) |
| \(\text{back triangle}\) | \(=\) | \(3\text{ edges}\) |
| \(\text{joining edges}\) | \(=\) | \(3\text{ edges}\) |
| \(3 + 3 + 3\) | \(=\) | \(9\) |
It has \(9\) edges.
| \(\text{triangular prism}\) | \(:\) | \(3 + 3 = 6\) |
| \(\text{square pyramid}\) | \(:\) | \(4 + 1 = 5\) |
The triangular prism has more vertices, \(1\) more than the square pyramid.
(i) Which has more flat faces?
(ii) Which one has a vertex?
| \(\text{cylinder}\) | \(:\) | \(2\text{ flat faces, no vertex}\) |
| \(\text{cone}\) | \(:\) | \(1\text{ flat face, 1 vertex}\) |
(i) The tin (cylinder) has more flat faces. (ii) Only the party hat (cone) has a vertex, at its point.
Common pitfalls
Frequently asked questions
What are faces, edges and vertices?
A face is a flat surface of a solid. An edge is a line where two surfaces meet; on a box it is straight. A vertex is a corner, where edges meet. We describe a 3D object by counting these three features.
Why does a drawing show fewer faces than the solid has?
A drawing shows a solid from one side, so some faces, edges and vertices are hidden at the back. A drawing of a cube shows only 3 of its faces. Count the hidden parts as well.
What is a vertex?
A vertex is a corner of a solid, where edges meet. One corner is a vertex and two or more are called vertices. The point at the top of a pyramid or a cone is a vertex too.
How do you count the edges of a prism?
Count the edges around one end, then the same number around the other end, then the edges that join the two ends. A triangular prism has 3 + 3 + 3 = 9 edges.
Can a solid have a curved edge?
Yes. Where the flat end of a cylinder or a cone meets its curved surface there is a curved edge. A cylinder has 2 curved edges and a cone has 1.
What is the difference between a flat face and a curved surface?
A flat face is a level surface, like the side of a cube. A curved surface is rounded, like the side of a cylinder or cone. Only flat surfaces are counted as faces.