Nails and staples work but are not recommended for high quality results. Properly installed threaded inserts are a good way to firmly secure polyethylene to many other materials. The highest quality lamination of polyethylene to polyethylene is in a compression molding press. When different color panels are used, the laminated panel becomes suitable for engraving or edge profiling. Various adhesives can also be used.
Adhesive purchase is increased when the surfaces are abraded.
Epoxy Glues, of many types, invisible glue line. Any of the adhesives listed for laminating will produce moderate strength edge joints depending upon the design and use of the construction. Hot melt adhesives may also be considered for this application. Polyethylene tack welds with a plastic welder, a soldering iron, a wood burning tool and even a clothes iron. Tack welds are produced when the hot tool is run along the seam where 2 pieces of polyethylene are touching producing a thin film of polyethylene joining the two pieces together.