Handkerchief n. : A piece of cloth, usually square and often fine and elegant, carried for wiping the face or hands.

Handkerchief n. : A piece of cloth shaped like a handkerchief to be worn about the neck; a neckerchief; a neckcloth.

Example:
Has anyone seen a Handkerchief butterfly folded in other patterns?

Taxonomy
handkerchief, Fold, puff, pocket square, silk handkerchief, cloth handkerchief, free encyclopedia, Bandanas, diagonally, Shell, pocket, decorative accessory, suit pocket, Kleenex, off-center, the Three, Three-point, corners.

Defination from the web:
handkerchief is also sometimes used as a purely decorative accessory in a suit pocket. The material of a handkerchief can be symbolic of the social-economic class of the user, not only because some materials are more expensive, but ...