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You might see some puzzles in this section that remind you of jigsaw puzzles - but the key difference here is that the edge features are compatible with several other potential mates and there are usually several other pieces that match any given piece.
The individual pieces can be easily arranged in many different ways that partially satisfy the rule - but overall there is usually only one total arrangement (or a relatively small number among all possible arrangements) that will completely meet the goal.
Jocelyn applied for a patent in Great Britian in 1892 (#3297 - I could not find a copy online - it is reproduced in Haubrich's About,...) in which they describe several triangular tile games and puzzles.
In his 1921 book New Mathematical Pastimes, Mac Mahon published some of the first material to treat edgematching puzzles with mathematical rigor.