---
tag: FXJ66Z6PQY
kind: concept
name: Net of a polyhedron
msc: [52B10, 52B05]
sources:
  - url: https://en.wikipedia.org/wiki/Net_(polyhedron)
same_as:
  wikidata: Q253829
  wikipedia: Net (polyhedron)
---

## Summary

A net of a polyhedron is a flat polygon that folds up into the surface of the polyhedron.
It is made of the faces of the polyhedron, joined along some of their edges.
It arises by cutting the surface along a spanning tree of edges and unfolding it into the plane without overlap.
Nets are used to build paper models, and whether every convex polyhedron has one is the open [[Dürer's conjecture|PEDBPRSV9V]].

## Explanations

### L1 human

Cut a cardboard box along some of its edges and flatten it: the flat piece is a net of the box.
The cross shape made of six squares is a net of the cube, and the cube has $11$ different nets in all.
The cuts must be chosen so that the surface stays in one piece and lies flat without the faces overlapping.