The idea, step by step
Count the folded object
A face is a flat surface, an edge is where two flat faces meet, and a vertex is a corner. For these polyhedra, count features of the folded solid, not every corner printed on its flat net.
A cube has 6 faces, 12 edges and 8 vertices. Edges belong to two faces, so counting four edges on each of six faces counts every edge twice.
Use shape and position clues
A triangular prism and a square pyramid both have five faces, but the face shapes differ. The prism has two triangles and three rectangles; the pyramid has one square and four triangles.
Two solids can also have the same feature counts but different sizes. A cube and a non-cube rectangular prism both have 6 faces, 12 edges and 8 vertices. Use dimensions or face shapes as well as counts.
A common trap
The corners visible on the flat net are all separate vertices of the solid.
Instead: Some corners meet during folding. Count where corners meet on the completed object.
See the thinking
Count shared edges
Why does a cube have 12 edges rather than 24?
- Six faces each show four edges: 6 × 4 = 24 face-edge appearances.
- Each physical edge is shared by two faces.
- 24 ÷ 2 = 12 distinct edges.
Five faces is not enough
A solid has five faces. Must it be a triangular prism?
- A triangular prism has two triangles and three rectangles.
- A square pyramid also has five faces: four triangles and one square.
- The number alone cannot choose between them.
Check your understanding
Which has more vertices: a cube or a square pyramid?
Show answer
A cube.
A cube has 8 vertices; a square pyramid has 4 base corners and an apex, making 5.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- State the faces, edges and vertices of a cube.3 marks
- A square pyramid has four base edges and four edges from the base corners to the apex. How many edges?1 mark
- A triangular prism has two triangular ends. Count its vertices.1 mark
- A solid has five faces: two triangles and three rectangles. Name it.1 mark
- Can a cube and a rectangular prism have the same face, edge and vertex counts? Explain.2 marks
- In the labelled cube net, will faces B and D touch along an edge after folding? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- State the faces, edges and vertices of a cube.3 marks
Count the folded solid; each edge is shared by two faces.
6 faces, 12 edges, 8 vertices. - A square pyramid has four base edges and four edges from the base corners to the apex. How many edges?1 mark
4 + 4 = 8.
8 edges. - A triangular prism has two triangular ends. Count its vertices.1 mark
Each end has 3 corners; 2 × 3 = 6.
6 vertices. - A solid has five faces: two triangles and three rectangles. Name it.1 mark
The matching triangular ends are joined by three rectangular sides.
Triangular prism. - Can a cube and a rectangular prism have the same face, edge and vertex counts? Explain.2 marks
Both have 6 faces, 12 edges and 8 vertices. Equal edge lengths distinguish a cube.
Yes. - In the labelled cube net, will faces B and D touch along an edge after folding? Explain.2 marks
They become opposite faces of the cube.
No.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Connect objects and two-dimensional nets; construct and explain spatial relationships.
Official curriculum source ↗