The Collaborative International Dictionary of English v.0.48:
Three-ply \Three"-ply`\, a. Consisting of three distinct webs inwrought together in weaving, as cloth or carpeting; having three strands; threefold. [1913 Webster]WordNet (r) 3.0 (2006):
three-ply adj 1: having a thickness made up of three layers or strands; "three-ply cloth"; "three-ply yarn"