Sheet grade polycarbonate (aka Lexan or Makrolon) and acrylic sheet (aka Lucite) are two of the most frequently used see-through plastics. Each of the two have benefits and drawbacks. Acrylic is shinier and polycarb is stronger. Acrylic is less expensive but easier to crack. Polycarb is more impact resisant but easier to scratch. They are both stronger and lighter than untempered glass.
