3D Shapes and Nets: Fold a Flat Pattern
Understand that a net is the flat pattern that folds into a solid with no gaps or overlaps, and that faces, edges and vertices are linked by Euler’s rule, faces plus vertices minus edges equals two.
Before you try
What if you laid six squares in a straight line? Would they fold into a cube?
Try it out
Interactive activity
Sign in to play
Use a Google account (yours or a parent’s) to unlock this simulator. We store only your name and email so your favourites and progress follow you.
Signing in needs an internet connection. Once you are signed in, simulators also work offline.
Free preview
Loading controls…
What happened?
Move a control to see what changes and why.
The folding is perfect, with no thickness and no overlap. Real card has thickness and needs tabs to hold together.
Something went wrong
This simulator could not load. Check your connection and try again.
Try these ideas
- Fold the cross net of a cube and count the faces as they close.
- Predict "no" for the straight line of six, then fold it and watch what happens.
- Check Euler’s rule for the square pyramid and the triangular prism.
Why it works
Cut a cardboard box along some edges, flatten it, and what you have is a net. Fold it back and every face must meet its neighbours exactly, with no gaps left open and no two faces landing on the same spot. Not every arrangement of six squares works: a 2 by 3 rectangle and a straight strip both fail, because the squares wrap round and collide instead of closing.
Solids are described by three counts: faces are the flat surfaces, edges are where two faces meet and vertices are the corners. For these solids they always satisfy Euler’s rule, faces plus vertices minus edges equals two. In this simulator you choose a solid, fold the net with a slider and rotate the result, and for cubes you predict whether each arrangement will work before folding it.
Check your understanding
Question 1 of 4
How many faces, edges and vertices does a cube have?
Does every arrangement of six squares fold into a cube?
What does Euler’s rule say for these solids?
How many faces does a square-based pyramid have?
Explain it in your own words
What changed? Why did it happen? Where might you notice this in everyday life?
What will you discover next?
Try Geometric Transformations: Move, Flip and Turn next.
For parents & teachers
- Unfold an empty cereal box and identify its net.
- Draw three different nets of a cube on squared paper and test them with scissors.
- Count faces, edges and vertices on real objects around the house.