Library/Geometry/Solid geometry/Sections, unfoldings, and frameworks/Properties of unfoldings

Properties of unfoldings

Overview
Important

An unfolding (or net) of a polyhedron is a connected, non-overlapping arrangement of all its faces in the plane, obtained by cutting along a set of edges so that the surface can be flattened without tearing or overlapping.

Important properties

  • Every face of the polyhedron appears exactly once in the net.

  • The net must be a single connected piece.

  • No two faces in the net overlap.

  • Folding the net along the original edges reconstructs the solid.

  • Different unfoldings are possible for the same polyhedron, depending on which edges are cut.