An ion mallet was a piece of equipment used in the game Parrises squares. It might also be called a Parrises mallet, or simply a mallet.
In 2373, The Doctor's holographic daughter, Belle, could not find her ion mallet to play a game of Parrises squares. He suggested that if she put it in her closet when she was finished, she'd know where it was. (VOY: "Real Life")
According to Harry Kim, being hit by Nausicaan heavyweight with a mean right hook was not nearly as bad as taking a Parrises mallet to the ribs. (VOY: "Tsunkatse")