3D Shapes: Faces, Edges & Vertices

Today's big idea

Every solid has faces, edges and vertices, and a curved surface is counted as a face.

Counting is safe only once you agree that a curved surface still counts as a face.

How it works

👀 What's going on?

A drawing of a box sits flat on the page. A real box does not. You can pick it up, turn it over, and run your finger along the lines where two sides meet. Counting those lines feels endless until you take the box one face at a time.

💡 Here's the trick

Look at the four solids above. A face is any surface you could rest a finger flat on, and a curved surface counts as one face too. An edge is the line where two faces meet. A vertex is a sharp point where edges come together. So the cube has 6 faces, 12 edges and 8 vertices, and a shoebox has exactly the same three counts.

🪄 How to do it

1.Count every surface on the solid above, the flat ones and the curved ones.
2.Trace each line where two surfaces meet, and count those as edges.
3.Find the sharp points where edges meet, and count those as vertices.

✍️ Try it

1.A shoebox is a cuboid. How many edges does it have?
2.A party hat is a cone and a tin of beans is a cylinder. How many FLAT faces do the two of them have altogether?

1.A cuboid has the same counts as a cube, so it has 12 edges.
2.The cone has 1 flat circle at its base and the cylinder has 2 flat circles. So the two of them have 3 flat faces, plus 2 curved ones.

⚠️ Watch out

You might be thinking that a curved surface cannot be a face, so a ball has no faces at all. In Class 3 the rule used here is that a curved surface does count. That gives a sphere 1 face, a cone 2 faces, and a cylinder 3 faces. Say that rule to yourself before you count, so your answer and the question agree.

🌟 Why this matters

Every tin, box and ball you handle is one of these solids. Their faces and edges decide how they stack and how they roll. A shop stacks cuboid cartons because flat faces sit still, and a ball rolls away because it has none.
Exam tip: Class 3 olympiad papers ask for a face, edge or vertex count almost every year.

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“How many faces does a cylinder have?”

1
Picture a cylinder
Think of a tin can. 🥫
2
Count the flat faces
A flat circle on top and one on the bottom = 2.
3
Add the curved face
The curved wall wrapping around counts as 1 more face.
4
Answer ✓
A cylinder has 3 faces

Now you try one — same steps, different story 👇

See it in action

⚡ Time to play!

Can you roll it? If it rolls, it has a curved face!

3D SHAPES · ROUND 1 OF 2 · SORT ALL 6

Quick check

✅ VERIFICATION

How many MORE edges does a cube have than a cone?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Triangle Classification

3 equal → equilateral. 2 → isosceles. 0 → scalene.

Concept 5 of 7 →