Scissor Blades

The Scissor Blades (片太刀鋏) are special weapons developed specifically to cut Life Fibers. They were created by Isshin Matoi as one single pair of scissors, the Rending Scissors (断ち斬りバサミ), and were divided in the moment of his murder.

Red Scissor Blade
Ryūko Matoi owns the red half of the Scissor Blade. It can expand into a longer sword (known as Decapitation Mode) or collapse into a normal size scissor half.

Purple Scissor Blade
Nui Harime owns the purple half of the Scissor Blade. Unlike Ryūko's half, it has a circular handle. It is as of yet unknown if it can also change size or form, though it is likely.

This half of the Scissor Blade seems to have changed color at some point, since it is shown to be red during Isshin's murder.

But as of Episode 21, it reveals that this Scissor Blade can become a double-bladed scythe of sorts.

Trivia

 * The boss character Mighty No. 7, from the upcoming video game Mighty No. 9, wields two halves of a giant red scissor thar bear a striking resemblance to the one wielded by Ryūko, indicating a possible reference to the Kill la Kill series.