GCSE · Geometry and measures
Prisms, pyramids and curved solids
Rotate different solids and compare faces, surfaces, edges and vertices.
Choose Prism, then change the number of sides from 3 to 8. Compare with Pyramid.
Scroll the diagram sideways to see every label.
| Count | Rule | Value |
|---|---|---|
| Faces | n + 2 | 7 |
| Edges | 3n | 15 |
| Vertices | 2n | 10 |
5-sided prism: 7 faces, 15 edges, 10 vertices.
- Flat faces
- 7
- Curved surfaces
- 0
- Edges
- 15
- Vertices
- 10
The smooth solids are rendered with small polygon panels for display; those panels are not mathematical faces or edges. We count a circular rim as an edge, and the cone apex as a vertex. The prism and pyramid bases are regular polygons.
Predict, test and explain
Step 1 of 3
Predict
Does a hexagonal prism have six faces?
Explore and compare
Choose the investigation above. Predict what will change before you move a control.
Try it in the simulation. Change one thing at a time.
Notes and saved values stay in this tab. They disappear when you reload.
Hints, self-check and connections
Try a self-check
Fixed values, separate from the diagram controls.
Does a hexagonal prism have six faces?
Hint
A prism with an n-sided end has n + 2 faces, 3n edges and 2n vertices.
Reveal answer
A prism with an n-sided end has n + 2 faces, 3n edges and 2n vertices.
Build an explanation
Hint 1
A prism with an n-sided end has n + 2 faces, 3n edges and 2n vertices.
Hint 2
Use the labels and units in the live model to check your method.
Hint 3
Explain which lengths, areas or volumes are being compared.
Worked example
This example uses fixed values, separate from the diagram controls.
State the faces, edges and vertices of a pentagonal pyramid.
- There is one pentagonal base and five triangular faces.
- There are five base edges and five edges to the apex.
- There are five base vertices and one apex.
Answer: 6 faces, 10 edges, 6 vertices.
Connect this idea
Watch out: A prism with an n-sided end has n + 2 faces, 3n edges and 2n vertices.