Editing Net (polyhedron) (section)

==Shortest path==
The [[geodesic|shortest path]] over the surface between two points on the surface of a polyhedron corresponds to a straight line on a suitable net for the subset of faces touched by the path. The net has to be such that the straight line is fully within it, and one may have to consider several nets to see which gives the shortest path. For example, in the case of a [[cube]], if the points are on adjacent faces one candidate for the shortest path is the path crossing the common edge; the shortest path of this kind is found using a net where the two faces are also adjacent. Other candidates for the shortest path are through the surface of a third face adjacent to both (of which there are two), and corresponding nets can be used to find the shortest path in each category.<ref>{{citation|title=How to Fold It: The Mathematics of Linkages, Origami and Polyhedra|first=Joseph|last=O’Rourke|publisher=Cambridge University Press|year=2011|isbn=9781139498548|pages=115–116|url=https://books.google.com/books?id=EbwNKD0xkUwC&pg=PA115}}</ref>

[[The spider and the fly problem]] is a [[recreational mathematics]] puzzle which involves finding the shortest path between two points on a cuboid.