Faces, edges and vertices of 3D solids
Foundation candidates must count and classify; Intermediate and Higher candidates apply Euler's formula.
📖Definition— Definitions
- Face: a flat polygonal surface (or a curved surface for a cylinder/cone/sphere).
- Edge: a line where two faces meet.
- Vertex: a corner where edges meet.
Standard prism counts
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Cuboid | 6 | 12 | 8 |
| Triangular prism | 5 | 9 | 6 |
| Hexagonal prism | 8 | 18 | 12 |
| Square-based pyramid | 5 | 8 | 5 |
| Tetrahedron | 4 | 6 | 4 |
Euler's formula (for convex polyhedra)
F + V = E + 2.
Quick check on a cube: 6 + 8 = 14 = 12 + 2 ✓.
This is a useful Higher cross-check when a question gives two of the three counts and asks for the third.
Curved-surface solids
- Cylinder: 3 surfaces (2 flat circular, 1 curved), 2 edges (the circular ones), 0 vertices.
- Cone: 2 surfaces (1 flat circular, 1 curved), 1 edge, 1 apex vertex.
- Sphere: 1 surface, 0 edges, 0 vertices.
Plans and elevations (links to G13)
Plan = top view; front elevation = view from the front; side elevation = from the side. Often paired with face/edge counting on Foundation papers.
WJEC exam tip
If a Higher question gives a "compound" solid (cuboid with a smaller cuboid removed) and asks for face/edge/vertex counts, sketch the result and count carefully — the cut introduces extra edges and vertices, and missing one is the most common error.
AI-generated · claude-opus-4-7 · v3-wjec-maths-leaves