Quadriceps or Quads: the major four-part large muscles of the front thighs primarily engaged in extending the leg at the knee.  The quadriceps femoris flexes the leg at the hip and extends the knee.

Quadriffis: Any quadruple somersault with a twist. 

Quad Twist:  A single layout somersault with four twists.  First performed in U.S. women's competition by Nastia Liukin.
 

Gymnastics Dictionary