  This paper considers an extension of origami geometry to the case of
"folding" a three dimensional (3D) space along a plane. First, all possible
incidence constraints between given points, lines and planes are analyzed by
using the geometry of reflections. Next, a set of 3D elementary fold operations
is defined, which satisfy specific combinations of constraints with a finite
number of solutions. The set consists of 47 valid fold operations, and
solutions to some of them are explored to determine their number and conditions
of existence.
