Any given surface that has been assigned a folding pattern and that pattern allows the piece to fold to form a plane contracting totally, without breaking or deforming, is considered "flat origami". Mathematical analyzes have proposed a series of axioms for the flat condition to occur in a specific pattern, and extensive research has studied the properties that it must have (J. Justin, T. Hull, M. Bern and B. Hayes). However, it has been Robert Lang who has summarized them more easily throughout his work, and specifically in the conference From Flapping Birds to Space Telescopes: The Modern Science of Origami dictating since 2005 in different universities and conventions on the subject of origami, mathematics, and science. These conditions  must be given for each of the vertices of the folds pattern, ie for the points where two or more fold lines are found.