Nets Workbench

Nets Workbench

Cut a solid along some of its edges, lay it flat, and fold it back up.

1Activity

2Solid

Family
Solid
Drag to turn it. Scroll or pinch to zoom.

3Counting the cuts

Faces
Hinges
Cuts

4About nets

Albrecht Dürer drew nets of polyhedra in his 1525 book on geometry, Underweysung der Messung, so readers could cut them out and fold them. Whether every convex solid can be cut along its edges into a net that lies flat without overlapping itself is still an open question, usually called Dürer's problem. Every solid tried so far has one, but no one has proved it must.

A cube has 11 different nets, and so does the octahedron. The tetrahedron has only 2. The dodecahedron and the icosahedron have 43,380 each.