🧊 3D Shapes

Faces, edges, vertices and Euler's formula!

📖 Learn
3D shape properties

✏️ Examples
Worked problems

🔬 Visualiser
Interactive tools

🎯 Practice
20 mixed questions

📖 3D Shapes

1. Faces, Edges and Vertices

Face – a flat surface of a 3D shape
Edge – a line where two faces meet
Vertex (vertices) – a corner where edges meet

Learn to count: faces → edges → vertices

2. Common 3D Shapes

Shape	Faces	Edges	Vertices
Cube	6	12	8
Cuboid	6	12	8
Triangular prism	5	9	6
Square pyramid	5	8	5
Tetrahedron	4	6	4
Cylinder	3	0*	0
Cone	2	0*	1
Sphere	1	0	0

*Cylinders and cones have curved surfaces — edges are not straight lines.

3. Euler's Formula

For any polyhedron (3D shape with flat faces):

Faces + Vertices − Edges = 2

Example: Cube → 6 + 8 − 12 = 2 ✓

Use this to find a missing value: if you know F and E, then V = 2 − F + E

4. Nets

A net is a flat shape that can be folded to make a 3D shape.

Cube net: 6 squares
Triangular prism net: 2 triangles + 3 rectangles = 5 faces
Square pyramid net: 1 square + 4 triangles = 5 faces

Faces in net = Faces on 3D shape

5. Classifying 3D Shapes

Prisms have two identical parallel ends (bases) and rectangular sides.

Pyramids have one base and triangular faces meeting at a point (apex).

Prism → named by its cross-section Pyramid → named by its base

✏️ Worked Examples

Example 1 – Count faces

How many faces does a triangular prism have?

2 triangular ends + 3 rectangular sides

Total faces = 5

Example 2 – Count vertices

How many vertices does a square pyramid have?

4 base corners + 1 apex = 5

Example 3 – Count edges

How many edges does a triangular prism have?

3 edges on each triangle + 3 side edges

3 + 3 + 3 = 9

Example 4 – Euler's formula

A shape has 6 faces and 12 edges. Find the vertices.

F + V − E = 2

6 + V − 12 = 2

V = 2 − 6 + 12 = 8

Example 5 – Net faces

How many faces does the net of a cube have?

Cube has 6 faces → net has 6 squares

🔬 3D Shape Visualiser

Shape Properties Lookup

Shape:

Euler's Formula Checker

Faces:

Edges:

Vertices:

Find Missing (Euler)

Faces:

Edges:

Exercise 1 – Faces

Enter the number of faces each shape has.

Exercise 2 – Vertices

Enter the number of vertices each shape has.

Exercise 3 – Edges

Enter the number of edges each shape has.

Exercise 4 – Euler's Formula: Find Vertices

Use F + V − E = 2 to find V.

Exercise 5 – Net Face Count

How many faces are in the net of each shape?