Folding nets into solids
About this app
Fold nets into cubes, pyramids, cylinders, cones and triangular prisms. Match faces and inspect why an invalid net cannot form the intended solid.
What a net is
Unfolding the surface of a solid flat into the plane, without overlaps, gives its net. The faces stay joined along shared edges, which act as fold lines. A cube has 11 distinct nets made of six squares. For a cylinder and a cone, the curved lateral surface unrolls into a rectangle and a circular sector respectively.
What the app shows
A slider folds the flat net along animated hinge edges into the 3D solid and back again. You can choose a cube, a square pyramid, a cylinder, a cone and a triangular prism. Click a face and it lights up in the net and on the solid at the same time. A puzzle net cannot be closed, and a badge tells you whether a net forms a solid.
Try it yourself
Fold the puzzle net slowly and watch where faces overlap or a side stays open. For the cylinder, work out which side of the rectangle becomes the circumference. Rotate the solid with the mouse to check which net faces end up opposite each other. Then pick another net and predict which edges will meet once it is folded.
Frequently asked questions
- How many different nets does a cube have?
- A cube has exactly 11 distinct nets, counting nets that are rotations or reflections of each other as the same. Each consists of six squares joined along edges.
- How can you tell whether a net folds into a cube?
- When folded, no two squares may overlap and each side of the cube must be covered exactly once. Four squares in a row are possible, five are not. It also helps to identify opposite faces: in a valid net, opposite faces never share an edge.
- What does the net of a cylinder look like?
- It consists of two circles for the top and bottom and a rectangle for the lateral surface. One side of the rectangle equals the height, the other equals the circumference 2πr.
- What does the app show?
- It folds the nets of five solids into the solid and back with an animation and links each net face to the matching face of the solid. An invalid net shows why not every arrangement of faces forms a solid.
Subject: School mathematics (Gymnasium)
More from School mathematics (Gymnasium)
- Tree diagram & path rules
- Binomial identities through geometry
- The number π
- Unit circle & sine curve
- Exponential growth & decay
- Ulm’s glass pyramid
- Equation balance
- Half-life & decay
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