Montauk Rug Collection. Flat-Weave Cotton Rugs. The imaginative talent of Safavieh s rug designers shines in the flat-weave cotton rugs in the Montauk Collection. These charming area rugs are filled with east coast cool in cotton-soft textures and evocative shades of sand sun and rolling surf. Classic Ikat tie-dye effects give a distinctive casual designer look that will complement the interior décor in homes from coastal to contemporary. Available in a wide selection of designs colors and sizes including small rectangular and hallway runners.