Faces, edges and vertices
Count the flat surfaces, the lines and the corners of a solid.
A brick
Pick up a brick or a matchbox. It is a cuboid. Its boundary is made of flat surfaces.
How many flat surfaces does a cuboid have?
What this lesson covers
The idea
Faces are the plane surfaces that form the boundary of a solid, edges are the line segments that form the sides of the faces, and vertices are the points where the edges meet.
A brick
Pick up a brick or a matchbox. It is a cuboid. Its boundary is made of flat surfaces.
How many flat surfaces does a cuboid have?
- 4
- 6
- 8
Mark every part
Choose Faces, Edges or Corners and tap them on the solid. Turn the solid with the sliders: some parts are hiding on the other side. Dashed lines are hidden edges.
Faces, edges, vertices
Faces are the plane (flat) surfaces that form the boundary of a solid. Edges are the line segments that form the sides of the faces, and vertices are the points at which the edges meet.
A cuboid or a cube has 6 faces, 12 edges and 8 vertices.
- Solid | Faces | Edges | Vertices
- Cuboid | 6 | 12 | 8
- Triangular prism | 5 | 9 | 6
- Square pyramid | 5 | 8 | 5
Notes
Faces are the flat surfaces that bound a solid, edges are the line segments that form the sides of the faces, and vertices are the points where the edges meet. A cuboid has 6 faces, 12 edges, 8 vertices.
Check yourself
Each of the 6 faces of a cuboid has 4 edges, but every edge is shared by two faces. How many edges does a cuboid have?
Answer: 12 edges
6 × 4 = 24 edge-sides, and every edge is counted twice, so 24 ÷ 2 = 12 edges.
How many faces does this triangular prism have?
Answer: 5 faces
3 rectangular faces + 2 triangular faces = 5 faces.
How many vertices does this square pyramid have?
Answer: 5 vertices
4 corners of the square base + 1 top point = 5 vertices.
Ravi looks at a cuboid on the table and says it has 3 faces. What did he miss?
- Faces are not flat. Faces are exactly the flat surfaces of a solid.
- He counted only the faces he could see. Three more are hidden: the back, the bottom and one side — correct. Yes! Turn the solid round. A cuboid has 6 faces, in 3 opposite pairs.
- A cuboid has no faces, only edges. The faces are the flat surfaces; edges are the lines where they meet.