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This article reviews the so-called "axioms" of origami (paper folding), whichare elementary single-fold operations to achieve incidences between points andlines in a sheet of paper. The geometry of reflections is applied, andexhaustive analysis of all possible incidences reveals a set of eightelementary operations. The set includes the previously known seven "axioms",plus the operation of folding along a given line. This operation has beenignored in past studies because it does not create a new line. However,completeness of the set and its regular application in practical origamidictate its inclusion. Formal definitions and conditions of existence ofsolutions are given for all the operations.

On the elementary single-fold operations of origami: reflections and incidence constraints on the plane