3D shapes
Faces, edges & vertices
Every 3D shape can be described by three counts: its flat surfaces, the lines where they meet, and its corners.
6 faces · 12 edges · 8 vertices
The three parts
FACE — a flat surface of the shape. EDGE — the line where two faces meet. VERTEX — a corner, where edges meet. (More than one is VERTICES.) A cube has 6 faces, 12 edges and 8 vertices.
Counting without missing any
The parts you cannot see are easy to forget. For a cube: you can see at most 3 faces at once, but there are 3 more hidden behind. Count them in pairs — top and bottom, front and back, left and right. Work systematically rather than counting what you happen to notice.
Prisms and pyramids
A PRISM has the same cross-section all along its length, with two matching end faces joined by rectangles. A triangular prism has 5 faces: 2 triangles and 3 rectangles. A PYRAMID has one base and triangular faces meeting at a point. A square-based pyramid has 5 faces: 1 square and 4 triangles. Both have 5 faces — so the number of faces alone does not identify a shape.
Naming from the base
Both prisms and pyramids are named after their base or cross-section. A pentagonal prism has pentagons at each end, so 7 faces in total: 2 pentagons and 5 rectangles. An octagon-based pyramid has 1 octagon and 8 triangles, so 9 faces. Count the sides of the base and the rest follows.
Worked examples
Faces, edges and vertices of a cube
- Faces: 6 — count them in pairs, including the hidden ones.
- Edges: 12 — each face has 4, but every edge is shared by 2 faces.
- Vertices: 8 corners.
Answer: 6 faces, 12 edges, 8 vertices
Faces of a triangular prism
- The two ends are triangles — that is 2 faces.
- Three rectangles join them.
- 2 + 3 = 5.
Answer: 5 faces
Faces of a square-based pyramid
- The base is 1 square.
- Four triangles rise to the point.
- 1 + 4 = 5.
Answer: 5 faces
Faces of a pentagonal prism
- A pentagon has 5 sides.
- The two ends are pentagons: 2 faces.
- Five rectangles join them.
Answer: 7 faces
Faces of an octagon-based pyramid
- The base is 1 octagon.
- An octagon has 8 sides, so 8 triangles rise from it.
Answer: 9 faces
Where you see this in real life
- A dice is a cube — 6 faces, which is why the numbers go up to 6.
- A tent is often a triangular prism: two triangular ends and rectangular sides.
- The pyramids at Giza are square-based pyramids with 5 faces including the base.
Key words
- Face
- A flat surface of a 3D shape.
- Edge
- The line where two faces meet.
- Vertex
- A corner where edges meet.
- Vertices
- More than one vertex.
- Prism
- A 3D shape with the same cross-section all along its length.
- Pyramid
- A 3D shape with a base and triangular faces meeting at a point.