Faces, edges, vertices of 3D solids
Foundation-tier territory on Edexcel 1MA1, examined on Paper 2F or 3F. The skill is identifying counts and surfaces of common 3D shapes.
Vocabulary
- Face: a flat surface of a polyhedron.
- Edge: a line where two faces meet.
- Vertex: a point where edges meet (corner). Plural: vertices.
- Surface: the total outer boundary (faces + curved surfaces if any).
Common solids — counts
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Cuboid | 6 | 12 | 8 |
| Triangular prism | 5 | 9 | 6 |
| Square-based pyramid | 5 | 8 | 5 |
| Tetrahedron | 4 | 6 | 4 |
| Cylinder | 2 flat + 1 curved | 2 | 0 |
| Cone | 1 flat + 1 curved | 1 | 1 (apex) |
| Sphere | 1 curved | 0 | 0 |
Euler's formula (polyhedra only)
F + V = E + 2.
Quick check: cube has 6 + 8 = 14, edges = 12, 12 + 2 = 14. ✓
Surfaces vs faces
A "face" in strict geometry is a flat polygon. A "surface" is more general — it includes curved surfaces (cylinder, cone, sphere).
Common Edexcel mark-scheme phrasing
- B1 for each correct count (face, edge, vertex).
- B1 for naming the solid.
- M1 for using F + V = E + 2 to check or find a missing count.
⚠Common mistakes— Common errors
- Counting curved surfaces as faces (only flat surfaces count as faces strictly).
- Confusing edges with vertices (an edge is a line; a vertex is a point).
- Saying a sphere has "1 vertex" — it has no edges and no vertices.
AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves