Jorge C. Lucero, On the elementary single-fold operations of Origami:
Reflections and incidence constraints on the plane,
Forum Geometricorum, 17 (2017) 207--221.
Abstract. This article reviews the so-called ``axioms'' of origami (paper folding), which are
elementary single-fold operations to achieve incidences between points and lines in a
sheet of paper. The geometry of reflections is applied, and exhaustive analysis of all
possible incidences reveals a set of eight elementary operations. The set includes the
previously known seven ``axioms'', plus the operation of folding along a given line.
This operation has been ignored in past studies because it does not create a new
line. However, completeness of the set and its regular application in practical origami
dictate its inclusion. Formal definitions and conditions of existence of solutions are
given for all the operations.
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