Kirigami (?) is a variation of origami that includes cutting of the paper (from Japanese "kiru" = to cut, "kami" = paper), rather than solely folding the paper as is the case with origami. It is also called "Kirui" (切り絵). From "Kiru"= to cut, "i"= picture.
Typically, kirigami starts with a folded base, which is then unfolded; cuts are then opened and flattened to make the finished kirigami. Kirigami are usually symmetrical, such as snowflakes, pentagrams, or orchid blossoms.
A difference between kirigami and the art of "full base" is that kirigami is made out of a single piece of paper that has been cut into a origami. Origami can be made of several pieces glued together.
Mon-Kirui is the Japanese art of paper cutting.