- published: 16 Jul 2015
- views: 277334
In geometry the net of a polyhedron is an arrangement of edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for models of polyhedra to be constructed from material such as thin cardboard.
For any given polyhedron that is unfolded into a net, many different equivalent nets can be formed depending on the choices of which edges are joined and which are separated.
It is a long-standing open question whether or not every convex polyhedron P (one without "dents" - in other words, all dihedral angles between the edges are ≤ 180 degrees) has a net: whether the surface P may be cut along edges and unfolded flat to a planar polygon (without overlap). (This system of edges is sometimes denoted as the polyhedron's unfolding.) The problem was first explicitly posed in a paper by Shephard. The history of and progress on this question is discussed in Part III of Geometric Folding Algorithms. If the restriction that the cuts be along polyhedron edges is relaxed to permit cuts through the interior of faces, then there are several known methods to cut and unfold a convex polyhedron to a planar polygon. For example, cutting along the cut locus of a point suffices.
NET or Net may refer to:
In computing and communication:
In business and finance as an antonym of gross:
NET as an acronym may refer to:
In broadcast and media:
In science and psychology:
In mathematics:
In other uses:
.net or .NET may refer to: