Recognition of Solids
65. The Cuboid's Structure · six faces, twelve edges, eight vertices
A cuboid always has six rectangular faces, twelve edges, and eight vertices.
A cuboid is a 3D solid bounded by 6 rectangular faces, with 12 edges and 8 vertices. Unlike a cube, the edges can have three different lengths — length, breadth, and height.
What this lesson covers
Try to break it
Drag the view handle to rotate the cuboid. Watch how the twelve edges and eight vertices become visible from different angles. Can you count them all?
How you build it
Construct a cuboid.
- Draw the front face ABCD as a rectangle.
- Draw the back face EFGH the same size, shifted up and to the right.
- Connect corner A to corner E.
- Connect corner B to corner F.
- Connect corner C to corner G.
- Connect corner D to corner H to complete the cuboid.
The proof, step by step
Prove that the solid is a cuboid with six rectangular faces.
- A cuboid has six faces, all of which are rectangles.
- A cuboid has twelve edges.
- A cuboid has eight vertices.
- Opposite faces of a cuboid are parallel.
- Adjacent faces of a cuboid meet at right angles.
Worked example
A cuboid has how many edges in total? Think about where the faces meet and count the line segments carefully.
A cuboid has 12 edges. These are the line segments where two faces meet.
- 6
- 8
- 12 — correct
- 10