Aircraft grade plywood, often Baltic birch, is made from 3 plies of birch, as thin as 1/16" thick in total, and is extremely strong and light.
In the UK single ply sheets of veneer were used to make stovepipe hats in Victorian times, so flexible modern plywood is sometimes known there as "Hatters Ply", although the original material was not strictly plywood, but a single sheet of veneer.