  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.
