The palmette is a design element said to resemble a cross section, or sometimes side view, of a woven stylized Lotus Flower. palmettes are found in many rugs, and take many different shapes/forms, colors and incorporation in design. It is not entirely uncommon a palmette would be a stand alone design element, although they sometimes may be woven in with an Islimi (eslimi) or other interconnected design elements.
Above: A silk Heriz from Sotheby's Auction April 10 & 11, 1981 (Lot 404)
Above: A Palmette design element from a very high grade Meshed/isfahan carpet (Below) made in Persia.