A very special type of polysquare puzzles is the set of 'square-puzzles', where all given shapes are squares with integral sidelength.
Reference
... Museum[?] Staffordshire Brindley Water Museum[?], Leek, Staffordshire Izaak Walton Cottage Museum[?] Suffolk Amber Museum[?], Southwold Beccles Museum[?] Ipswich ...