Concept 5 of 6
The Solid Family: Faces, Edges and Vertices
Today's big idea
Every solid has three counts: its faces, its edges and its vertices.
A cube has 6 faces, 12 edges and 8 vertices; a cylinder is curved with 0 vertices.
How it works
👀 What's going on?
A ball, a tin and a dice feel completely different in your hand. To describe any solid exactly, you count it three ways: its faces, its edges and its corners.
💡 Here's the trick
Look at the table above. A face is a flat or curved surface, an edge is a line where two faces meet, and a vertex is a sharp corner. A cube has 6 faces, 12 edges and 8 vertices. A square pyramid has fewer of each, with 5 faces, 8 edges and 5 vertices.
🪄 How to do it
- 1.Find your solid in the table above and count its faces first.
- 2.Count the edges, the lines where two faces meet.
- 3.Count the vertices, the sharp corners where edges meet.
✍️ Try it
Count the faces, edges and vertices of a triangular prism. Then do the same for a cylinder.
The triangular prism has 5 faces, 9 edges and 6 vertices. The cylinder is curved, so it has 3 faces, 2 edges and no vertices. Curved solids break the tidy pattern.
⚠️ Watch out
You might count a curved surface as many faces, or miss it altogether. A cylinder's curved side is one single face, and a sphere is one curved face with no edges and no corners.
🌟 Why this matters
Boxes, dice, tents and buildings are all solids, and naming their faces, edges and vertices is how you describe a shape you cannot hold. Line up the counts for the flat-faced solids and a pattern begins to show, one you will turn into a rule in Class 5.
Exam tip: Count faces, then edges, then vertices in the same order every time, so you never lose your place on a busy solid.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“How many faces, edges and vertices does a square pyramid have?”
- 1
Faces first
One square base plus 4 triangular sides: 1 + 4 = 5 faces.
- 2
Then edges
4 edges around the base, and 4 sloping up to the tip: 4 + 4 = 8 edges.
- 3
Then vertices
4 corners on the base, and 1 sharp tip on top: 4 + 1 = 5 vertices.
- 4
Answer ✓
A square pyramid: 5 faces, 8 edges, 5 vertices.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Pick a solid, then count its faces, edges and vertices. Solve 3 to finish.
Faces
Edges
Vertices
Solved 0 / 3 solids
Quick check
✅ VERIFICATION
How many vertices does a triangular prism have?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Cube Nets
Plus shape folds. Straight line doesn't. 11 valid nets total.