The flowers I make are called Kusudama. (like this one below)
The Japanese kusudama (薬玉; lit. medicine ball) is a paper model that is usually (although not always) created by sewing multiple identical pyramidal units (usually stylized flowers folded from square paper) together through their points to form a spherical shape. Alternately the individual components may be glued together. (e.g. the kusudama in the lower photo is entirely glued, not threaded together) Occasionally, a tassel is attached to the bottom for decoration.
Kusudama originate from ancient Japanese culture, where they were used for incense and potpourri; possibly originally being actual bunches of flowers or herbs. The word itself is a combination of two Japanese words kusuri, Medicine, and tama, Ball. They are now typically used as decorations, or as gifts.
The kusudama is important in origami particularly as a precursor to the modular origami genre. It is often confused with modular origami, but is not such because the units are strung or pasted together, instead of folded together as most modular construction are made.
It is, however, still considered origami, although origami purists frown upon using its characteristic technique of threading or gluing the units together, while others recognize that early traditional Japanese origami often used both cutting (see thousand origami cranes or senbazuru) and pasting, and respect kusudama as an ingenious traditional paper folding craft in the origami family.
Modern origami masters such as Tomoko Fuse have created new kusudama designs that are entirely assembled without cutting, glue or thread except as a hanger.